TELESCOPE ARRAYTECHNICAL DESIGN REPORT

January 17, 2000

Contents
1 Physics
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Experimental Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Cosmic Rays above GZK energy . . . . . . . . . . . . . . . . . . . .
1.2.2 Cosmic Rays around 1018 eV . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Chemical composition . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Physics of Extremely High Energy Cosmic Rays . . . . . . . . . . . . . . .
1.3.1 Astrophysical sources of the highest energy cosmic ray . . . . . . .
1.3.2 Interaction with CMBR . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Magnetic ﬁeld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.4 Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . .
1.4 Physics of EHE Neutrinos and γ-rays . . . . . . . . . . . . . . . . . . . . .
1.5 Physics of Active Galactic Nuclei Neutrino . . . . . . . . . . . . . . . . .

1
1
3
3
6
7
8
9
10
12
12
16
21

2 TA Detector
2.1 Conceptual Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Site and Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The Telescope and Optics . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Photomultiplier and Camera . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Calibration of PMT . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Design of PMT Camera . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Electronics and Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 System requirement and overview . . . . . . . . . . . . . . . . . . .
2.5.2 Front-end Electronics System . . . . . . . . . . . . . . . . . . . . .
2.5.3 Signal Finder Module . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Intersite Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Data acquisition and online system . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2 Slow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.3 Structure of online software . . . . . . . . . . . . . . . . . . . . . .
2.7.4 Run Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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27
28
31
36
36
41
42
45
45
47
51
53
54
54
56
56
57
58

i

ii

CONTENTS

3 Atmospheric monitoring
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Components of the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The Molecular Component . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The Aerosol Component . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Monitoring the Atmosphere - Local measurements . . . . . . . . . . . . . .
3.4 Atmospheric Monitoring - longer range . . . . . . . . . . . . . . . . . . . .
3.5 Cloud monitor by Infra-red imaging detector . . . . . . . . . . . . . . . . .
3.6 Atmospheric Monitoring System for Telescope Array . . . . . . . . . . . .

61
61
62
63
64
65
67
72
73

4 Physics Simulation and Expected Results
75
4.1 The TA Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.1 The TA event generator . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1.2 Signal and background pulse simulator . . . . . . . . . . . . . . . . 77
4.2 The Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.1 The center-of-gravity constraint . . . . . . . . . . . . . . . . . . . . 78
4.2.2 Fast reconstruction for initial guess . . . . . . . . . . . . . . . . . . 79
4.2.3 Reconstruction using the pulse proﬁle . . . . . . . . . . . . . . . . . 80
4.2.4 Reconstruction of longitudinal shower development . . . . . . . . . 82
4.3 Aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Resolutions of Energy, Angle and Xmax . . . . . . . . . . . . . . . . . . . . 87
4.4.1 Accuracy of arrival direction and Xmax . . . . . . . . . . . . . . . . 87
4.4.2 Determination of energy . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4.3 Atmospheric correction . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4.4 Uncertainty of measurement . . . . . . . . . . . . . . . . . . . . . . 94
4.5 Detection of EHE Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6 Identiﬁcation of EHE γ-rays . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.6.1 Simulation of hadronic and γ-ray shower . . . . . . . . . . . . . . . 99
4.6.2 The Longitudinal development of γ-ray induced showers and its identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.7 The Observational Power to Distinguish Diﬀerent Models . . . . . . . . . . 105
4.8 Detection of Active Galactic Nuclei Neutrino . . . . . . . . . . . . . . . . 107
5 Collaboration

115

6 Cost and Schedule

117

References

118

Chapter 1
Physics
1.1

Introduction

This proposal describes the Telescope Array project which will make a major advance inthe study of the highest energy cosmic rays, γ-rays and neutrinos. The Telescope Array
will explore the high energy phenomena in the universe, the acceleration of high energy
particles, non-thermal processes, and search for the relics of the Hot Big Bang. At present,
we know that cosmic ray particles with extraordinary energies, 30J to 50J exist [1, 2, 3, 4].
These are macroscopic energies and this is the highest energy radiation in the universe so
far experimentally studied by human beings. An eﬃcient particle accelerator or particle
factory in the universe is required as a source of these particles. These studies are strongly
related not only to astrophysics, but also to elementally particle physics and cosmology.
The study of cosmic ray origins began with the initial discovery by Hess in 1912. The
existence of natural radiation was known before this, but he showed that it comes fromthe sky. After the discovery, extensive eﬀorts for the measurement of cosmic rays havebeen carried out with various methods. In particular, the discovery of the air shower
phenomena (cascade showers which reach the ground, induced by very energetic cosmicrays) by P. Auger was very important. At present, we know their energy extends overmore than 13 decades from 107 eV up to 1020 eV. Since the initial discovery, the studyof their origin has been a most important issue. Their energy density in our Galaxy is∼ 1 eV/cm3, which is comparable with energy densities of the photon ﬁeld and magnetic
ﬁeld in our Galaxy. Ginzburg and Syrovatskii (1964) suggested Super Novas as the originof galactic cosmic rays. At the present time, many observations, including the chemical
abundance of cosmic rays and gamma ray observations, appear to support this hypothesis.
The production of cosmic rays below 1015 eV is likely to be explained with the ﬁrst order
Fermi shock acceleration at supernova remnants.
At present, the most interesting topic in the cosmic ray physics is the study of the highest
energy cosmic rays. Experimental data accumulated so far show increasing inconsistency
with the conventional models for cosmic ray origin based on acceleration of charged particles. We expect to see an end of the high energy cosmic ray spectrum at 6 × 1019 eV, due
to the resonance production of hadrons with the cosmic microwave background radiation(CMBR), what is called the Greisen-Zatsepin-Kuzmin (GZK) cutoﬀ [5]. Most striking,however, is the clear evidence for the extension of the cosmic ray energy spectrum above
1

2

CHAPTER 1. PHYSICS

the GZK cutoﬀ discovered by AGASA and the Fly’s Eye experiment, and recently conﬁrmed by preliminary data from HiRes. Furthermore, the propagation length of cosmic ray
particles above the GZK cutoﬀ energy is limited to within 50 Mpc from our Galaxy. The
magnetic ﬁeld of the Galaxy and of inter-galactic space is not strong enough to bend the
trajectory of these particles more than a few degrees. Sources for particles with energies
above the GZK cutoﬀ energy should thus be relatively close by and particles will point backto these sources. However, no possible astrophysical sources (accelerators) at the arrival
direction of these particles within 50 Mpc of the Earth were found.

FIG. 1.1: The energy spectrum of cosmic ray [6].

1.2. EXPERIMENTAL STATUS

1.2

3

Experimental Status

In Fig. 1.1, we show the cosmic ray energy spectrum over a very wide energy range. The
spectrum can be roughly represented by a single power law with exponent of −2.8. However,
we can see small kinks at 1016 eV (knee) and 1019 eV (ankle).
At the knee, the galactic cosmic ray leakage from our Galaxy may increase and theenergy dependence of the cosmic ray life time becomes stronger. The Larmor radius ofparticles with 1016 eV in our Galaxy is expected to be ∼ 3(1/Z) pc for the particle withcharge Z. The scale ∼ 1 pc corresponds to the typical size of a magnetic ﬁeld turbulencein the disk of our Galaxy. We also expect the maximum acceleration energy in a Super
Nova Remnant to be ∼ 1014 × Z eV [7]. Detailed studies of the knee region of the spectrum
were carried out. So far, however, there are many possible interpretations of the knee,
including leakage from the galactic disk, energy limits of the acceleration mechanism, or
new additional components (this model interprets the knee as an additional bump). In allcases, we can say these cosmic rays must originate in our Galaxy.
The ankle is interpreted as the cross over energy from a galactic cosmic ray spectrum
to an extragalactic one. The Larmor radius of cosmic rays in our Galaxy is calculated tobe ∼ 3 kpc (E/1019 eV)(1/Z), thus these cosmic rays propagate more freely than at lower
energy. The deﬂection angle in the propagation of these particles is less than a radian.
Therefore, if we assume galactic sources, we expect very strong cosmic ray anisotropy (theanisotropy amplitude could be ∼ 100% ). However, the small measured anisotropy above
ankle (only upper limits are obtained from experiments) naturally requires an extra galactic
component. The depth of the shower maximum in the atmosphere (Xmax ) is sensitive tothe chemical composition. The Xmax study by Fly’s Eye suggests a gradual change ofchemical composition from heavy components to light components around 1018.5 eV [8].
If this is true, it is a strong evidence for the cross over from a galactic component to an
extragalactic one.

1.2.1

Cosmic Rays above GZK energy

Figure 1.2 shows the energy spectrum above 1018.5 eV observed by AGASA experiment[4]. For reference, we have superposed the expected GZK energy spectrum assuming theuniform source distribution in the Universe. Eight events are observed above 1020 eV. Theenergy of giant air showers observed by AGASA is estimated by the particle density S(600)at a distance of 600m from the shower axis. This is known to be a good energy estimator[9]. The conversion factor from S(600) [m−2] to primary energy E0 [eV] is derived fromsimulation [10] to be
E0 = 2.0 × 1017 × S(600)1.0 .
In Fig. 1.3, the Fly’s Eye stereo spectrum is shown [8]. There is no events above 1020
eV because the aperture for stereo data is too small. The result is statistically consistent
with AGASA if we consider the exposure diﬀerences. The kink (ankle) at 1018.5 eV is seenclearly. In the stereo observation, the shower geometry is obtained as an intersection of
two detector-shower planes. The energy is estimated by two eyes. The energy resolution
is obtained experimentally to be 20%. The position of the ankle is slightly lower than
AGASA. The cosmic ray intensity is lower than AGASA by factor of 1.4. These eﬀects

CHAPTER 1. PHYSICS

4

26

J(E) E 3 [m -2 sec-1 sr -1 eV 2 ]

10

25

10

4

3
1

10 6
2
24

10

Uniform sources

23

10

10

19

10

20

Energy [eV]FIG. 1.2: The energy spectrum observed by AGASA. The vertical axis is multiplied by E 3 .
Error bars represent the Poisson upper and lower limits at 68% and arrows are 90% C.L.
upper limits. Numbers attached to points show the number of events in each energy bin.
The dashed curve represents the spectrum expected for extragalactic sources distributed
uniformly in the Universe, taking account of the energy determination error. The primary
spectrum is assumed ∝ E −2.3 .

FIG. 1.3: The cosmic ray energy spectrum obtained by Fly’s Eye stereo observation. The
number of events above 1019 eV is 60. The exposure is about 1/5 of AGASA. The lackof events above 1020 eV is consistent with AGASA result, if we take the exposure into
account. The clear kink (ankle) is seen around 1018.5 eV.

1.2. EXPERIMENTAL STATUS

526

J(E) E3 [m-2 sec -1 sr-1 eV 2 ]10

AGASA (900217-980831)
Fly’s Eye (mono)(1999Aug)
HiRes
3

25

10

8

1

3
4

2

24

10

Uniform sources

23

10
18.5

19.0

19.5

20.0

20.5

21.0

LOG (Energy [eV])FIG. 1.4: The energy spectrum obtained by AGASA, original Fly’s Eye and HiRes monocular observation (preliminary). Three data are consistent each other.
can be explained by the diﬀerence in energy resolution and systematics. For example, if wereduce the AGASA energy by 15 % or increase the FE stereo energy by 15 %, we obtainmuch better agreement between two experiments.
In Fig. 1.4, we have shown the energy spectra obtained by AGASA, Fly’s Eye monocularexperiment and HiRes monocular experiment(preliminary). The HiRes data has a similar
aperture to AGASA. The three data sets are consistent each other within statistical errors
above 1019 eV. Diﬀerences below 1019 eV reﬂect the diﬀerent energy resolution and energy
scale systematics between the three experiments. Diﬀerences in energy scale were magniﬁed
in this plot by E 3 weighting. In total, we have observed 16 events above 1020 eV. The number of events, one from monocular Fly’s Eye, seven from HiRes and eight from AGASA are
consistent, if we take into account the exposure of each experiment. The energy spectrum
clearly extends beyond 1020 eV with no GZK cutoﬀ. It is not clear with present statistics
whether there is any structure in the spectrum (for example, a small valley at 1020 eV).
The arrival direction distribution of the highest energy cosmic rays above 4 × 1019 eV isshown in Fig. 1.5 in the equatorial coordinates [11]. Small dots and squares show events
between 4× 1019 eV and 1020 eV and above 1020 eV, respectively. The events above 1020 eVcorresponds to the pure super-GZK particles, and if they are hadrons their sources should becloser to the Earth than 50 Mpc. The energy 4×1019 eV is the lower threshold energy of the
expected pile produced by the GZK eﬀect up. Events above this energy may still come fromthe same sources as the super-GZK events. Their energies have been decreased by inelastic
interactions. If we assume an E −2.3 source energy spectrum, we expect 50 % or more ofthese event to originally have energies above the GZK cutoﬀ. They appear to be distributed
uniformly over the observable sky. We have carried out several tests for anisotropy but

CHAPTER 1. PHYSICS

6

Equatorial Coordinates

o

+60

Dec
o

+30

24

h

0
h

12

GC

h

RA

Galactic Plane

-30
-60

o

o

Supergalactic Plane
FIG. 1.5: The arrival direction of the highest energy cosmic rays on the equatorial coordinates observed by AGASA.
could not ﬁnd any large scale structures in this distribution. However, we found one triplet
and three doublets of events clustering within an angular resolution (2.5◦ circle) as indicatedshadowed circles. The chance probability for this clustering eﬀect was evaluated by Monte
Carlo simulation and found to be Pch = 0.0032. No outstanding astronomical objects havebeen found in the directions of these clusters, although an interacting galaxy called VV141
was found to lie in the direction of the triplet at 100 Mpc away.

1.2.2

Cosmic Rays around 1018 eV

In order to explore the origin of galactic cosmic rays, a harmonic analysis in Right Ascension
was carried out using about 216,000 events observed by AGASA [12]. This is a reliable
method to search for global anisotropy of the cosmic-ray arrival direction distribution. The
amplitude, the phase (peak direction in Right Ascension), and the Rayleigh power k were
determined in each diﬀerential energy bin as shown in Table 1.1. A Rayleigh power k ∼ 14
was found at energy bin E5. This is surprisingly high, corresponding to a chance probabilityof 2.5 × 10−6 .
Table 1.1: The ﬁrst harmonic analysis in Right Ascension.
Bin
E4
E5
E6
E7

Energy Range [EeV]
1/2 – 1.0
1.0 – 2.0
2.0 – 4.0
4.0 – 8.0

#
56658
29207
10129
2769

Amplitude [%]
0.5
4.2
2.0
3.3

Phase [◦ ]
k
272
0.42
297
12.9
256
1.10
256
0.76

Pprob
0.65
2.5 × 10−6
0.33
0.46

Declination[degree]

1.2. EXPERIMENTAL STATUS

7

90

4
3

30

-30

2

anti G.C.

1
0
G.C.

-1
-2

-90

-3
300

200
100
Right Ascention[degree]

0

FIG. 1.6: The statistical signiﬁcance of the deviations of the arrival direction distributionof the cosmic rays above 1018 eV on the equatorial coordinates (obtained by AGASA) [12].
In Fig. 1.6 the arrival direction distribution in the equatorial coordinates obtained by
AGASA is shown. The ﬁgure shows the statistical signiﬁcance of the deviations fromisotropic expectation. Here, the energy region of 1018 eV ∼ 1018.4 eV is selected whichcorresponds to the maximum Rayleigh power k-value. Note that we cannot observe eventswith declination less than −25◦ , as long as we use showers with zenith angles less than60◦ . In this ﬁgure, we have chosen a circle of 20◦ radius to evaluate the excess. In thesigniﬁcance map, a 4.5 σ excess (obs./exp. = 506/413.6) near the Galactic Center region
can be seen. In contrast, near the direction of anti-Galactic Center we can see a deﬁcit in
the cosmic ray intensity (−4.0σ). An event excess from the direction of the Cygnus regionis also seen with 3.9σ (obs./exp. = 3401/3148). This anisotropy can be considered asclear evidence for the existence of galactic cosmic rays up to 1018 eV. Similar, though lessstatistically compelling results have recently been published by the Fly’s Eye experiment.
They show a 3 σ enhancement from the galactic plane in an energy bin near 1018 eV.

1.2.3

Chemical composition

Figure 1.7 shows the Xmax distribution measured by the Fly’s Eye experiment [8]. Recently,
this result has been conﬁrmed by the HiRes prototype and CASA, MIA hybrid experiments[13]. An unusually large elongation rate (energy dependence of Xmax ) is found. One
expect 60 g/cm2 increase per decade of energy from Monte Carlo simulation if one has an
unchanging hadronic composition. However, the Fly’s Eye experiment observed 80 g/cm2
per decade between 1017 eV and 1019 eV. This can be interpreted as being due to a change
in chemical composition from heavier to lighter. In the AGASA experiment, the muoncomponent is measured by shielded detectors. Looking at the correlation of ρμ (600) andCHAPTER 1. PHYSICS

8

S(600), no signiﬁcant evidence for a rapid composition change was found [14]. However,an analysis of both experiments using a the same hadronic model (Sybill) by B.Dawson
and R.Meyhandan [15], suggests that a gradual chemical composition change from heavier
to lighter between 1016 eV and 1019 eV is compatible with both experimental results.

FIG. 1.7: The average Xmax as a function of primary energy obtained by Fly’s Eye. Two
upper and lower lines correspond to pure proton and pure iron primaries. The energy
dependence of Xmax can be interpreted as a change in the chemical composition fromheavier to lighter between 1017 eV and 1019 eV.

1.3

Physics of Extremely High Energy Cosmic Rays

The interesting features of the highest energy cosmic ray study can be summarized asfollows.
– Astrophysical sources of the highest energy cosmic rays are limited. Only GRBs(Gamma
Ray bursts), AGNs (Active Galactic Nucleuses), Colliding galaxies and Radio galaxy
lobes are possible sources. However, AGNs and Radio galaxy lobes within 50 Mpc
are almost ruled out by recent observations of super-GZK events since they do not
point back to any such object.
– The propagation length of super-GZK particles is limited due to the interaction with
CMBR. About 50 Mpc is a limiting value for the radius of the GZK horizon.

1.3. PHYSICS OF EXTREMELY HIGH ENERGY COSMIC RAYS

9– The bending of protons due to the magnetic ﬁeld in our Galaxy and inter galactic
space should be small. There is thus the possibility to open the new astronomical
window on the universe using hadronic particles above the GZK energy.
– Fundamental science. Cosmic rays with 1020 eV energy are the highest energy radiation so far observed. The current energy scale, 1020 eV, is beginning to approach the
GUT scale energy 1024 –1025 eV. The observation of the highest energy cosmic rays
may be of signiﬁcant importance to elementally particle physics and cosmology.

1.3.1

Astrophysical sources of the highest energy cosmic ray

In Fig. 1.8, the possible cosmic ray sources are plotted on an object size versus magnetic
ﬁeld strength map [16]. In the Fermi acceleration or one shot acceleration models, we always meet with the minimum condition for the attainable maximum energy: Rg < Robj /2,i.e., the Gyro radius of accelerated particle should be smaller than the object size. Since

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

10 km
1AU

1pc

1kpc

1Mpc 1Gpc

Size

FIG. 1.8: The astronomical objects as cosmic ray sources. They are plotted on size andmagnetic ﬁeld strength map. The minimum requirement for the sources, Larmor radius
should be smaller than accelerator size, is shown by the line. The most promising source
for the highest energy cosmic ray is GRBs.

CHAPTER 1. PHYSICS

10

gyro radius is proportional to the particle momentum, this equation give us the maximum
acceleration energy for each object. At the same time, we need to consider the coolingor energy loss process of cosmic ray particles in these objects, for example, synchrotron
radiation, and photo-pion production. In compact sources (or in the strong magnetic ﬁeldcase), synchrotron radiation becomes important, because the energy loss rate is proportional to B 2. On the other hand, in large acceleration systems (≥ Mpc), the acceleration
time becomes relatively larger and we need to consider photo-pion production process with
CMBR. Using these arguments, we can discard neutron stars (extremely high B condition),and galactic clusters (photo-pion cooling becomes dominant) as candidates for sources of
the highest energy cosmic rays.
The GRBs, AGNs, and radio galaxy lobes alone remain as source candidates. Most
promising are the GRBs, because AGNs and radio galaxy lobes are just on the acceleration
boundary and no such candidates have been identiﬁed with the recent observation of superGZK events. GRBs on the other hand, can solve this problem. There is a constraint on
GRB models from the arrival direction distribution of super-GZK particles. The GRB rate
in our Universe is estimated ∼ 2/day from BATSE gamma ray detector observations. Thisvalue can be rewritten as 0.0013–0.0026/(100 Mpc)3 yr. The typical propagation delayof charged cosmic ray with respect to light is 100–1000 yrs (this will be explained later)
due to the scattering by the magnetic ﬁeld in the inter-galactic space. Therefore, we will
see the GRBs occurred in the last 100–1000 yrs within the GZK horizon (50–100 Mpc).
The number of GRBs contributing to the cosmic ray ﬂux is thus estimated to be at most,
5 ∼ 10 in this space-time volume and we expect only several independent GRBs (arrival
direction) for cosmic rays. At present about 20 super-GZK events are recorded, and we
see no clusters in their arrival direction distribution. This gives a constraint on GRBs
source model. However, if we consider the beaming eﬀect in the GRB ﬁreball model, thisproblem may be resolved since we can increase the number of independent GRBs in the
GZK horizon.
As mentioned above, we have constraints on the conventional astronomical source (“Bottomup”) models from observations. “Top-down” models can evade many of these constraints.
They explain the super-GZK particles as decay products from heavy relics such as, monopoleannihilation (monopolonium collapse), cosmic string decay, decay of necklaces, etc. In any
such models, we expect a hard energy spectrum and gamma ray dominant chemical compositions. These scenarios can solve the current problem. They exhibit no GZK eﬀect,
uniform arrival direction distribution of super-GZK particles, and no identiﬁcation of anastronomical counter part. The big bonus from these scenarios is the presence of a large
neutrino ﬂux. These models will be discussed in detail in the following sections.

1.3.2

Interaction with CMBR

An important feature of the highest energy cosmic rays is their interaction with CMBR
[5]. In Fig. 1.9, we show the energy spectrum modiﬁed by the interaction with CMBR[17]. The left ﬁgure shows the spectrum expected from a one-source model. Several lines
correspond to diﬀerent propagation lengths. If one bright source dominates in the cosmic
rays observed at the Earth, we expect such spectra. The right ﬁgure shows the expectationfrom a uniform source model, each line corresponds to the diﬀerent evolution parameters1.3. PHYSICS OF EXTREMELY HIGH ENERGY COSMIC RAYS

11

3

10

10

dF 3
[Arbitrary Unit]
dE E

0.008

-1

0.057

10

0.032

dF 3
[Arbitrary Unit]
dE E

0.004

1

0.1

0.016

0.5
-2

10

2

10

1
2
3
10

4
5

1
1.0

-1

-3

10

17

10

18

10

19

10

10

20

ENERGY [eV]

10

21

10

22

10

17

10

18

10

19

10

10

20

10

21

10

22

ENERGY [eV]FIG. 1.9: The energy spectrum modiﬁcation by the interaction with CMBR. The left ﬁgureshows the spectrum expected from one source model. Several lines correspond to diﬀerent
propagation lengths. The right ﬁgure shows the expectation from the uniform source model,
each line corresponds to the diﬀerent evolution parameter.

FIG. 1.10: The history of the energy of cosmic ray particle traveling the CMBR sea. It is
worthy to note that the particle observed at the Earth with super-GZK energy has greater
energy at the source. For example, if we observe cosmic rays of 3 × 1020 eV from the sourcewith distance of 30 Mpc, it should have 1021 eV at the source.

CHAPTER 1. PHYSICS

12

of cosmic ray production. Except for a nearby one source model, in both cases, we expect
a clear GZK cutoﬀ below 1020 eV.
The evolution of the energy of a cosmic ray as it travels through the CMBR is shownin Fig. 1.10. This plot shows that the original cosmic ray energy at the source should behigher than that observed at the Earth, especially for the particles above 1020 eV. For
example, 2 × 1020 eV or 3 × 1020 eV corresponds ∼ 1021 eV at the source, if we assume thepropagation length of 30 Mpc. Of course, this evaluation depends on the source distance,
and we require that the accelerator has a large enough Emax (maximum attainable energy).

1.3.3

Magnetic ﬁeld

Another important feature of cosmic ray propagation is their interaction with the magnetic
ﬁeld in our Galaxy and inter-galactic space. Generally the knowledge for magnetic ﬁeld islimited, especially in the inter-galactic space. The galactic magnetic ﬁeld can be measured
by the Faraday Rotation Measure of linearly polarized radio signals and by the Dispersion
Measure of pulsar signals. The strength of magnetic ﬁeld in the disk is estimated to be
2μG. The scale height of magnetic ﬁeld strength of our Galaxy is obtained to be 1.0–1.4
kpc by recent observations [18, 19, 20]. Recently the magnetic ﬁeld inside local clusters ofgalaxies is measured and their strengths are found to be a few μG [21, 22]. In the void
region, only the upper limit for the magnetic ﬁeld strength, 10−9 G is obtained so far.
Figure 1.11 shows the cosmic ray propagation in our Galaxy. In this calculation, an antiproton is ejected from the Earth. At 1018 eV, the cosmic ray particles couple with magnetic
ﬁeld strongly. However, at higher energy, they travel more freely and the trajectories
become linear.
Figure 1.12, left panel, shows the deﬂection angles of cosmic rays in the inter-galactic
space and in the Galaxy, as a function of energy. The time delay relative to propagation
time for light is shown in the right panel. Here, we assumed the magnetic ﬁeld strength of
1 nG and the coherent scale of 1 Mpc in the inter-galactic space. Typical time delay forsuper-GZK particles is 100–1000 years in 30 Mpc propagation. Therefore, even if GRBs
are sources of super-GZK particles, we may not see any clear temporal correlation between
the GRBs and super-GZK particles with limited observation time.
With the knowledge of the propagation, we can discuss the GRBs model in more detail.
Figure 1.13 shows the cosmic ray energy spectrum expected from GRBs source model [23].
Since the time delay is energy dependent, higher energy particles arrive earlier and thus weobserve cosmic rays with limited energy range at a certain time. Older GRBs contributein lower energy region, and closer GRBs contribute as larger ﬂux. If we assume stronger
magnetic ﬁeld, we expect wider energy spectrum for each GRBs.

1.3.4

Beyond the Standard Model

Many conventional models, based on the acceleration of charged particles by the shockwaves in magnetic ﬁelds, were developed. These include AGNs [24], hot-spots of type II
radio galaxies [25, 26], colliding galaxies [27, 28], pulsars [29], supermassive blackholes [30],galactic wind termination shocks [31], gamma ray bursts [23, 32], and etc. However, there
are serious problems for these models, insuﬃcient acceleration, and signiﬁcant energy losses

1.3. PHYSICS OF EXTREMELY HIGH ENERGY COSMIC RAYS

13

Y[kpc]

10

0

-10

-10

0

10

X[kpc]

Y[kpc]

10

0

-10

-10

0

10

X[kpc]

Y[kpc]

10

0

-10

-10

0

10

X[kpc]

FIG. 1.11: The ray trace of proton particles in our Galaxy. In this calculation, the antiproton is ejected from the Earth. At 1018 eV, the cosmic ray particles couple with magnetic
ﬁeld strongly. At higher energy, they travel more freely and the trajectories become linear.

14

CHAPTER 1. PHYSICS

FIG. 1.12: Left: The deﬂection angle is shown as a function of primary cosmic ray energy.
Upper and lower lines corresponds to propagation in the extra galactic space, and in our
Galaxy, respectively. Here, we assumed magnetic ﬁeld strength of 1 nG for the extra
galactic space. Right: The time delay through the propagation relative to light.

FIG. 1.13: The cosmic ray energy spectrum expected from GRBs source model. The cosmic
ray observation period of 10 yrs is almost delta function if we consider the typical timedelay of propagation, 100–1000 years. Since the time delay is energy dependent, we observe
cosmic rays with limited energy range at certain time period. Realistic simulation predicts
the spiky energy spectrum for each GRB. Older GRBs contribute in lower energy region,and closer GRBs have larger ﬂux. If we assume stronger magnetic ﬁeld, we expect wider
energy spectrum for each GRBs.

1.3. PHYSICS OF EXTREMELY HIGH ENERGY COSMIC RAYS

15

by accelerated particles within the acceleration site as mentioned above. These models
usually employ extreme values in parameters to explain the extension of the spectrum
beyond 1020 eV.
There is another set of models with completely diﬀerent approaches to explain the superGZK particles. These are the so-called Top Down models in which EHE CR are produced
in decays of superheavy particles (X-particles) [33, 34, 35, 36, 37, 38]. These new particles
have to decay into ordinary particles during present era, and they have to be heavy enoughand their number density and life time suﬃcient to explain the present EHE CR ﬂux.
For example, the decay of cosmic strings may produce X particles (GUT gauge bosons),
through the intersection of cosmic strings, cusp evaporation, self-intersection, or collapse of
closed loops. Then X-particles decay into quarks and leptons while quarks give hadron jets.
We expect a photon and neutrino dominant composition in the ﬁnal products. Anotherpossible source of X-particles is the annihilation of primordial monopole-antimonopole pairs(monopolonia) [39] or cosmic strings with monopoles (so-called necklace) [40, 37].
Another proposed concept is long-lived primordial X-particles. The X-particle must havea suﬃcient life time to survive until the present epoch and must decay at some ﬁnite ratein the present. These possibilities are discussed in the literatures [41, 42, 43].
Another possible scenario is that the primary particles are not ordinal particles. The
possibility of neutrino [44, 38, 45] and supersymmetric hadrons S 0 [46] have been discussed.
A diﬀerent approach is to assume that the special relativity is violated. This has been
discussed by S.Coleman and S.L.Glashow [47]. In deriving the GZK cutoﬀ, Lorentz invariance is assumed for γ = 1011 , however, there is no independent experimental conﬁrmationthat special relativity is valid at such high γ factor.
Hereafter, we will discuss in detail about some important scenarios.
– Superhigh energy neutrinos possibly emitted from powerful far-away sources could
collide with nearby cosmological neutrinos with a mass of 0.1 ∼ 1 eV generatingcosmic rays beyond the GZK cutoﬀ energies [45, 48]. Extensive numerical calculation
have shown this mechanism could explain the observed energy spectrum without
violating the constraints obtained by high energy γ-rays, cosmic rays, and neutrino
observations if the maximum neutrino energy reaches to ∼ 1022 eV and the relicneutrino dark matter is clustered on the supercluster scale (∼ 5 Mpc) [44].
· Positive Aspects
This model relies on only well accepted physics. Observations of the highest
energy cosmic rays could prove the massive cosmological neutrinos which arerelics from the big bang.
· Negative Aspects
The sources must have a dense photon target to supply the required high neutrino luminosity and to absorb primary γ-rays and protons. The model is valid
only if neutrinos have masses heavier than 0.1 eV.
· This model predicts
protons and γ-ray photons with energies beyond 1020 eV whose ﬂux intensities

CHAPTER 1. PHYSICS

16

are comparable each other. High ﬂuxes of neutrinos are expected (see the next
section) whose arrival directions might have correlations with the γ-rays comingfrom directions of far-away astrophysical sources.
– Cold dark matter trapped in the Galactic halo might be origin of most energetic
cosmic rays [49, 40]. An energy spectrum without cutoﬀ is naturally expected because
the particles are created inside our Galactic halo.
· Positive Aspects
If true, the study on extremely high energy astroparticles would probe the
WIMPs, the most favored scenario in the dark matter hypothesis.
· Negative Aspects
There are too many free parameters to ﬁt the observations.
· This model predicts
anisotropy associated with the Galactic center, but the AGASA data above
1019 eV does not support this [11]. More statistics is required to investigate
anisotropy at 1020 eV, which would be a real test for this idea.
– If monopoles and/or cosmic strings (so called topological defects) were formed insymmetry-breaking phase transitions in the early universe, they may have produced
EHE particles with energies up to the GUT scale (typically ∼ 1016 GeV) through theircollapse or decay, with leptons and hadronic jets emitted from the supermassive “X”
particles [33]. This Top Down models are attractive because they predict injection
spectra which are considerably harder than shock acceleration spectra and which can
extend to an energy of ∼ 1016 GeV, typical in GUTs [38].
· Positive Aspects
These models provide us with a way to probe the very early Universe when
the GUT energies matched the thermal temperature of the Space. The absenceof obviously identiﬁable astronomical objects is not a problem because the X
particles need not be associated with any visible astrophysical sources.
· Negative Aspects
The model is exotic, relying on high energy physics notions that are far fromproven.
· This model predicts
the comparable ﬂuxes of protons and photons with energies beyond 1020 eV
extending up to 1025 eV or even greater, and high ﬂuxes of EHE neutrinos (seethe next section). No astrophysical counterparts should be expected.

1.4

Physics of EHE Neutrinos and γ-rays

Neutrinos have uniquely advantageous characteristics in the Extremely High Energy (EHE)
Astrophysics: they can penetrate cosmological distances in the Universe and their trajectories are not deﬂected because they have no electric charge. They carry information about
extremely high energy production processes, even in the early Universe.

1.4. PHYSICS OF EHE NEUTRINOS AND γ-RAYS

17

ENERGY SPECTRUM
2

-30

10

Cosmic Ray Nucleons-1[m sec sr eV ]

1

-35

10

dF
dE

-2

-1

-1

Eelectron Neutrinos

1. m=4.0 Zmax=2.0
2. m=4.0 Zmax=4.0

16

10

18

10

20

10

22

10

ENERGY [eV]FIG. 1.14: Energy spectra of the EHE neutrinos produced by the GZK mechanism [17].
The maximum energies of cosmic ray protons at acceleration sites are assumed to be 1021
and 1022 eV respectively.
The most conventional process to create cosmic EHE neutrinos is a production by the
GZK mechanism: the decay of photopions produced by EHE cosmic ray protons colliding with the cosmic thermal background photons [5, 50]. Figure 1.14 presents the GZK
neutrino spectra under several assumptions concerning the EHE cosmic ray sources [17].
The neutrino ﬂux below 1019 eV becomes higher as the parameter m characterizing source
evolution and the “turn-on time” zmax , the boundary to which a spatial distribution of
EHE cosmic ray emitters extends are increased. It is also seen that there is sensitivity to
the value of maximum accelerated energy of EHE cosmic rays in the ﬂux of neutrinos. The
ﬂux of neutrinos above 1019 eV depends strongly on the maximum energy of EHE cosmic
rays, while the cosmic ray spectral shape itself does not depend strongly on the maximum
energy. The ﬂux of GZK neutrinos can be a good probe to estimate the turn-on time,
evolution parameter, and the maximum energy of primary EHE cosmic rays.
The EHE neutrinos will also open up another interesting possibility: Astrophysical beams
to search for cosmological relic neutrinos. Their energies may be high enough to collidewith the 1.9 K cosmic background neutrinos to produce a signiﬁcant neutrino cascade

CHAPTER 1. PHYSICS

18

dN
dlogE

0

0

νe
-5

-5

νμ

νe

νμ
γ

p

e

ντ
10

ντ
γ

p
12

e

Log (Energy x (m ν ) ) [GeV]
1eV

14

10

12

Log (Energy x (m ν ) ) [GeV]
1eV

14

FIG. 1.15: Energy spectra of the particles in super-high energy neutrino induced cascades
after the propagation of 1 Mpc. The left panel shows the case when primary electron neutrino energy is 1022 × (mν /1eV) eV and the right panel shows the case of 4 × 1021 (mν /1eV)
eV, the energy at the Z boson resonance.
due to the enhanced interaction probability at Z-boson resonance [51, 52]. The cascading
increases the total EHE neutrino ﬂux because a single EHE neutrino can spawn multiple
EHE neutrinos [52] as shown in Fig. 1.15. If neutrinos have a mass as suggested in theatmospheric neutrino observation by the Super-K, a dip structure with a slight enhancementof the ﬂux at lower energies will appear in the EHE neutrino spectrum [53], which may
provide the observational signature of relic neutrinos.
The neutrino cascading would provide the visible eﬀects on the “Top Down” (TD) scenarios which supposes EHE cosmic rays are created directly as decay or interaction productsof particles with masses much higher than the observed energies rather than being accelerated from lower energies. In the current versions of such (TD) scenarios, predominantly
γ-rays and neutrinos are initially produced at extremely high energies by the decay of supermassive elementary “X” particles related to some grand uniﬁed theories (GUT). Such X
particles could be released from topological defect relics of phase transitions which might
have been caused by spontaneous breaking of GUT symmetries in the early Universe [33].
The EHE neutrinos with energies extending up to the GUT scale give rise to signiﬁcantneutrino cascades.
Similar to neutrinos, the γ-rays and electrons produced by X particle decay initiate
electromagnetic (EM) cascades on low energy radiation ﬁelds such as the CMB. The highenergy photons undergo electron-positron pair production (PP; γγb → e− e+ ), and at energies below ∼ 1014 eV they interact mainly with the universal infrared and optical (IR/O)
backgrounds, while above ∼ 100 EeV they interact mainly with the universal radio background (URB). Electrons produced in this process transfer most of their energy to a background photon via inverse Compton scattering or sometimes via triplet pair production(eγb → ee+ e− ). Since the EHE γ-ray attenuation length does not decrease with energy(as is the case for protons), there is no cutoﬀ feature in the spectrum [54]. This leads tothe prediction of a dominant γ-ray ﬂux at energies above the GZK cutoﬀ. Neutrinos andγ-rays driven by the cascades on the cosmological background ﬁelds are major players in
EHE energy range.

1.4. PHYSICS OF EHE NEUTRINOS AND γ-RAYS

19

FIG. 1.16: Energy spectra of nucleons, γ-rays and neutrinos for the TD model with mX =1016 GeV and the decay mode X → q + q, assuming the high URB version and an EGMF
of 10−10 G [38]. Thick and thin lines represent the SUSY and no-SUSY fragmentation
function, respectively. 1 sigma error bars are the combined data from the Haverah Park[55], Fly’s Eye [8] and the AGASA [4] experiments above 1019 eV. Also shown are piecewise
power law ﬁts to the observed charged CR ﬂux below 1019 eV, the EGRET measurementof the diﬀuse γ-ray ﬂux between 30 MeV and 100 GeV, and experimental neutrino ﬂux
limits from Frejus [56] and Fly’s Eye [57], as well as projected neutrino sensitivities of the
future Pierre Auger [58] and NASA’s OWL [59] projects.

FIG. 1.17: Same as Fig. 1.16, but for the pure neutrino decay mode with no EGMF. Shownare the maximal EHE neutrino ﬂuxes allowed by the EGRET limit for mX = 1014 GeV(thick lines) and mX = 1013 GeV (thin lines). A mass of neutrinos is assumed to be 1 eV
here.

20

CHAPTER 1. PHYSICS

Figure 1.16 shows the ﬂuxes of some TD scenarios along with current observational
constraints on and projected sensitivities of some future experiments to γ-ray and neutrino
ﬂuxes [38]. The cosmic ray primaries with energies above 1020 eV can be γ-rays as shownin the ﬁgure. EHE neutrino ﬂux is ∼ two orders of magnitude higher than that of cosmic
ray hadrons at 1020 eV range.
Another interesting scenario involves the pure neutrino decay modes, also shown in
Fig. 1.17 for mX ≤ 1014 GeV [38]. Here, the γ-rays and nucleons are produced as secondaries
from the interactions of these EHE neutrinos with the relic neutrinos. Because γ-rays andnucleons above 100 EeV must have been produced within a distance of λa  few Mpc fromthe observer, their ﬂux is dominantly produced by interactions with the locally clusteredneutrinos. The outstanding bumps in the neutrino spectra are created by the neutrinocascades discussed above. Their detection would be the observational evidence of theneutrino dark matter.

FIG. 1.18: Energy spectra of nucleons, γ-rays and neutrinos for the scenario of “Governor
Neutrino” described in the text [44]. Neutrino sources are assumed to be distributed
homogeneously up to z = 3.
It has been pointed out that collisions of EHE cosmic neutrino beams with ∼ eV mass
neutrino dark matter themselves would explain the observed cosmic ray energy spectrum[45, 48], regardless of the nature of the neutrino sources if the maximum neutrino energy
reaches to the Z boson pole region and the dark matter is clustered on the Supercluster scale by amounts consistent with expectations [44] because the secondary protons andγ-rays produced by the neutrino cascade as shown in Fig. 1.15 can constitute a hard component of the observed cosmic rays without a GZK cutoﬀ. Powerful remote AGNs and/or
cosmological gamma ray bursts (GRBs) can be the sites to radiate EHE neutrinos. In thismodel EHE neutrino could “govern” all the other EHE particle intensities. Figure 1.18
shows the spectra of the “secondary” cosmic ray protons and γ-rays with the “primary”
neutrinos in this model [44]. A slight bump appears in the neutrino spectra because of
the low energy secondary neutrinos in the cascade. It predicts γ-ray ﬂuxes comparable orlarger than nucleon ﬂuxes above 1020 eV. Detection of neutrinos and primary γ-rays witharrival directions correlated each other associated with the remote astronomical objects
will lead to indirect search for signatures of neutrino dark matter.

1.5. PHYSICS OF ACTIVE GALACTIC NUCLEI NEUTRINO

21

In summary, observations of EHE neutrinos and γ-ray photons at the EHE range would
probe the astrophysics involving the phase transitions in the early Universe and/or theneutrino dark matter. Whether there are remarkable astronomical objects within theirarrival directions is a key factor to distinguish the diﬀerent models. Consequently thedetector capability of reconstruction of neutrino and γ-ray events with excellent angularresolution would be crucial to this study. The resolutions expected in the Telescope Array
will be discussed in Chapter 3.

1.5

Physics of Active Galactic Nuclei Neutrino

Active Galactic Nuclei (AGN) are a class of galaxies (Quasars, Blazars, Radio Galaxies,
Seyferts, Optically Violent Variables, BL Lac’s) which are characterized by large radio
output and by large redshifts. They appear as star-like objects, indicating extremely highpower output: 1042 to 1048 erg/s, many orders of magnitude greater than our own Galaxy
and thus the most luminous objects known in the Universe. Their engines must not only
be powerful, but extremely compact because their high energy luminosities are observed
to ﬂare by over an order of magnitude over time periods as short as a day [60]. They
are assumed to consist of a super-massive black hole, having as much as 109 solar masses
surrounded by an accretion disk and a torus of hot gas. Jets are often seen along the axis of
the disk. In a uniﬁed scheme of AGN, they correspond to Radio Loud AGN viewed from a
position illuminated by the cone of a relativistic jet [61]. The 3rd EGRET catalog of highenergy γ-ray sources [62] contains 66 high conﬁdence identiﬁcations of AGN and 27 lower
conﬁdence potential ones. All belong to the blazar subclass, mostly Flat Spectrum Radio
Quasars, while the rest are BL-Lac objects [63]. Blazars appear also to be able to explain
about 25% of the diﬀuse extragalactic γ-ray emission [64, 65]. TeV γ-ray emission has been
observed from three blazars, the BL-Lac objects Mrk 421, Mrk 501, and 1ES2344+514[66]. The data therefore strongly suggests that the highest energy photons originate in jets
beamed to the observer [67, 68, 69].
Confronted with the challenge of explaining a relatively ﬂat multi-wavelength photon
emission spectrum which extends to TeV energy, models have converged on the blazar
model shown in Fig. 1.19. Particles are accelerated by Fermi shocks in bunches of mattertraveling along the jet with a bulk Lorentz factor of order γ∼10. Ultra-relativistic beamingwith this Lorentz factor provides the natural interpretation of the observed superluminal
speeds of radio structures in the jet [70]. In order to accommodate bursts lasting a dayin the observer’s frame, the bunch size must be of order ΓcΔt∼10−2 pc, where Γ is the
Doppler factor which for observation angles close to the jet direction is of the same orderas the Lorentz factor [61]. These bunches are more like sheets thinner than the jet’s widthof ∼ 1 pc.
Most theoretical work on γ-ray emission in AGN jets involved electron acceleration andinverse Compton scattering, and these models will predict no neutrinos. In electron blazar
models the multi-wavelength spectrum consists of three components: synchrotron radiation
produced by the electron beam on the magnetic ﬁeld in the jet, synchrotron photons
Compton scattered to high energy by the electron beam to produce the highest energy
photons in the spectrum [71]. The seed photon ﬁeld can be either external, e.g., radiatedCHAPTER 1. PHYSICS

22

JET

γ

WIND

BH

DISK

FIG. 1.19: Geometry of AGN.
oﬀ the accretion disk, or result from the synchrotron radiation of the electrons in the jet,synchrotron-self-Compton models. These models have problems. In order to reproduce theobserved high energy luminosity, the accelerating bunches have to be positioned very close
to the black hole. The photon target density is otherwise insuﬃcient for inverse Compton
scattering to produce the observed ﬂux. The same dense target will eﬃciently absorb thehigh energy photons by γγ collisions. The natural cutoﬀ therefore occurs in the 10–100
GeV region [71]. Finally, in order to prevent the electrons from losing too much energy
before producing the high energy before producing the high energy photons, the magnetic
ﬁeld in the jet has to be artiﬁcially adjusted to less than 10% of what is expected fromequipartition with the radiation density.
In some of the proton blazar models energetic protons interact with radiation via pion
photoproduction [72]. Because of reduced energy loss, protons can produce the high energy
radiation further from the black hole. The favorable production-absorption balance makes
it relatively easy to extend the high energy photon spectrum above 10 TeV energy, evenwith bulk Lorentz factors that are signiﬁcantly smaller than in the inverse Compton models.
These models are turn out to describe the multi-wavelength spectrum of the AGN [73, 74].
Because the density of photons is still much higher than that of target protons, the highenergy cascade is initiated by the photoproduction of neutral pions by accelerated protons
on ambient light via the Δ resonance. The protons collide either with synchrotron photons

1.5. PHYSICS OF ACTIVE GALACTIC NUCLEI NEUTRINO

23

produced by electrons [73], or with the photons radiated oﬀ the accretion disk [74].
Model-independent evidence that AGN are indeed cosmic proton accelerators can beobtained by observing high energy neutrinos from the decay of charged pions, photoproduced on the Δ resonance along with the neutral ones. The neutrino spectrum can now be
calculated from the observed gamma ray luminosity. We recall that approximately equalamounts of energy are carried by the four leptons (e+ ,νμ , ν e ,ν μ ) that result from the decay chaine, π + → νμ μ+ → e+ ν e ν μ . The cross sections for the processes pγ → pπ 0 and
pγ → nπ + at the Δ resonance are the approximate ratio of 2 : 1. Thus a ratio of neutrino
to γ-ray luminosities (Lν , Lγ ) of 1 : 3. The ratio is reduced when taking into account thatsome of the energy of the accelerated protons is lost to direct pair production (pγ → pe+ e− )but the correction should be small (∼ 10%).
We assume that the target photon density spectrum is described by a E −1 power low andthe number of target photons above photoproduction threshold grows when the protonenergy is increased. For a standard non-relativistic shock, protons are accelerated to a
power low spectrum with spectral index 2, the threshold eﬀect implies that the spectral
index of the secondary neutrino ﬂux is also a power low with an index ﬂattened by 1 as aresult of the increase in target photons at resonance when the proton energy is increased:


Eν
dNν
= Norm ·dEν
EνM ax−1,here EνM ax is the maximum neutrino energy which can be derived by Fermi’s shock acceleration theory assuming parameters around AGN. Therefore the normalization Norm canbe obtained by: E M axνdEν Eν

2
LγdNν
 Norm · EνM ax  Lν .
dEν
4

Assuming that the high energy γ-ray ﬂux from Mrk 421 results from cascading of the
gamma ray luminosity produced by Fermi Accelerated protons, we obtain the neutrino ﬂux
from the measured value of Lγ of 2 × 10−10 TeV cm−2s−1 [67, 68, 69]:
dNνEνM ax∼ 5 × 10−17 cm−2 s−1Eν
dEν1018 eV−1.

This calculation reveals that the neutrino ﬂux is essentially determined by the value forEνM ax .
In shock acceleration the gain in energy occurs gradually as a particle near the shock
scatters back and forth across the front gaining energy with each transit. The protonenergy is limited by the lifetime of the accelerator and the maximum size of the emitting
region R [75]: Ep < KeBRc, where B is the magnitude of the ambient magnetic ﬁeld which
can be calculated from equipartition with the electrons whose energy density is measured
experimentally yielding B ∼ 5 Gauss, the size of accelerator R is determined by the
duration, of order 1–2 day, over which the high energy radiation is emitted: R = Γtc ∼ 0.01–
0.02 pc, and the constant K depends on the details of diﬀusion in the vicinity of the shock.
In the case that the eﬃciency by which power in the shock is converted into acceleration

CHAPTER 1. PHYSICS

-3

2

-2 -1

-1

log10(E dI/dE [GeV cm s sr ])

24

-4

SZ-P
H-Z

-5

ST-SA

M

-6

ATM-ν

-7

P

-8

-9

-10

-11

-12

13

14

15

16

17

18

19

20
21
log10(E[eV])FIG. 1.20: Diﬀused neutrino ﬂux predictions from AGN.
of particles reach values close to 1, the maximum proton energy reaches: EpM ax = eBRc =5×1019 eV for B ∼ 5 Gauss and R ∼ 0.02 pc. The average energy carried by the neutrino in
the photoproduction and decay chain, is roughly 1/20 of the parent proton energy. Finally1
EpM ax ∼ 1018 eV .
the maximum neutrino energy is estimated to be EνM ax = 20
First models for neutrino production in AGN assumed shock acceleration in the AGN
cores and predicted relatively ﬂat ﬂuxes up to energies of about 1015 eV [76, 77]. There ishowever recent evidence that the GeV to TeV γ-ray emission observed from AGN corresponds to the blazar class as described above [78, 74, 79]. In some proton blazar models[79], only interactions of protons with radiation via pion photoproduction (pγ) would leadto neutrino production as described above. The other models [77, 76, 78, 74] count contributions both from the processes of (pγ) and (pp) which makes a signiﬁcant change ofthe spectrum in the lower energy region below 1015 eV. Diﬀuse neutrino ﬂux predictions
assuming the neutrino productions in the cores and in the jets are illustrated in Fig. 1.20
assuming Blazars appear to be able to explain about 25% of the diﬀuse γ-ray emission
and the electron and muon neutrinos contribute to the ﬂux but approximately the electron
neutrino ﬂux is a factor of two below the muon neutrino for all cases. From the assumptions

1.5. PHYSICS OF ACTIVE GALACTIC NUCLEI NEUTRINO

25

the ﬂuxes have been corrected from the original estimates [77, 76, 78, 74, 79]. In Fig. 1.20,
the range of atmospheric neutrino background as the zenith angle changes from 0◦ to 90◦[80], which appears to have so large spectral index that it cannot largely contribute toneutrino detection in the higher energy region above 1015 eV in any proton blazar models.
Neutrino produce showers in most interactions with the atmosphere. In the interactions,the target nucleons break up and the debris behaves as a group of hadrons that results
in a shower similar to those induced by hadronic cosmic rays in both neutral and charged
current interactions. If the neutrino is of electron ﬂavor the interactions with the electrons
have in general much smaller cross sections and can be disregarded except for the resonant electron-antineutrino electron interaction which dominates just for neutrino energies
around the resonant value of 6.4 PeV. The potential of TA to detect neutrinos of energies
more than 1016 eV through deeply penetrating air showers will be described in the later
section. Assuming some simple conservative trigger and selection requirements we obtain
the acceptance for deeply penetrating air showers as induced by high energy neutrinos andwe then give the expected event rates for a variety of AGN neutrino ﬂuxes as predicted in
diﬀerent models with are used here.
In conclusion, using the great sensitivity for extremely high energy neutrinos with the TA
detector, we can establish or reject the proton AGN model by detecting enough statistics
of AGN neutrinos and conﬁrming the coincidence with EGRET catalog of high conﬁdence
identiﬁcations for AGN. Furthermore, we can resolve the location of the proton accelerationnear the core or in the jet of AGN by testing the spectrum slopes as predicted in Fig. 1.20.

Chapter 2
TA Detector
2.1

Conceptual Design

The Telescope Array (TA) detector has been planned in order to draw a decisive conclusionon the mysterious origin of the extremely high energy cosmic rays. For this purpose, thedetector is required to have much larger aperture for super-GZK events than the present
day detectors. Also it should provide a particle identiﬁcation as well as an accurate determination of energy and arrival direction for primary cosmic rays.
The TA is a giant array of air ﬂuorescence detectors to satisfy these requirements. It
measures the UV ﬂuorescence of molecular nitrogen generated by the air shower particles
by large aperture telescopes. The observation of the whole shower development process inthe atmosphere enables the unbiased determination of the energy by the total absorption
calorimetry. A single air shower event will be observed simultaneously by 2 or more telescopes separated by more than 40 km, which allows an accurate determination of the event
geometry by the stereo event reconstruction.
The particle identiﬁcation of the primary particle is made by measuring the longitudinaldevelopment of the shower in the atmosphere. The depth of the shower maximum (Xmax)
is a good parameter for the identiﬁcation. This technique has a great advantage to discriminate gamma rays and neutrinos from other primary cosmic rays, which is the essential
feature of the experiment to identify the origin of EHE cosmic rays.
The eﬀective aperture of TA is approximately 5,000 km2 sr for 1020 eV particles assuming
a 10 % duty factor. It is 30 times larger than the existing AGASA ground array, and isan order of magnitude larger than the new ﬂuorescence telescope, HiRes. The future
generation ground array, the southern hemisphere Pierre Auger in Argentina, will haveabout the same acceptance.
The Telescope Array consists of 10 measurement stations installed in the West Desertof USA, near Salt Lake City, Utah. Each station is separated by 30–40 km and is deployed as shown in Fig. 2.1. The Fly’s Eye, HiRes and Utah Seven Telescopes group havebeen operating in the vicinity. Three out of 10 TA stations cover the planned northernhemisphere Auger detector, forming a large hybrid detector each having about the sameeﬀective acceptance for the EHE cosmic rays.
Each TA station is equipped with two rings of 20 imaging telescopes arranged in a circleof φ ∼30 m. The upper ring covers the elevation angle of 3◦ –18.5◦ and the lower ring27

CHAPTER 2. TA DETECTOR

28

FIG. 2.1: Station deployment of Telescope Array.
covers 18.5◦ –34◦ . A total of 40 reﬂecting telescopes with 3 m φ mirror is installed in astation. It covers 360◦ in azimuth and is sensitive to the cosmic rays falling within ∼ 60
km of the station. The cosmic rays above 1018.5 eV will be measured simultaneously by 2
or more stations and the stereo reconstruction will be applied. The cosmic rays below thisthreshold will be measured by a single station down to 1016 eV. These low energy eventsare close to the station and a monocular reconstruction of the geometry will be applied.
The development of the shower in the atmosphere is recorded by the imaging camera
placed on the focal plane of each telescope. It is composed of a 16 × 16 matrix of hexagonal
photomultipliers (PMTs). The ﬁeld of view covered by one PMT (pixel size) is approximately 1◦ × 1◦ . The signal from the PMT is digitized every 200 ns with a 12-bit resolution.
The dynamic range of 16 bits is achieved by the 2-range (H/L) digitization scheme. Eachchannel is equipped with a digital signal processor (DSP) and a sophisticated signal ﬁnding
algorithm will be executed for generating a trigger.
A steerable laser is placed at the center of each station. It will be used to determine theextinction coeﬃcient of the ﬂuorescence light along the transmission path to the telescope.

2.2

Site and Infrastructure

The Telescope Array requires a vast extent of land with good atmospheric transparency,
good weather and dark night sky free from the light pollution by human activities. At
the same time, contradictory conditions of good infrastructure such as the access road,
power line, computer network and communication are desirable for the construction andoperation of the experiment.

2.2. SITE AND INFRASTRUCTURE

29

We have selected the West Desert of USA, 100–200 km south west of Salt Lake Cityin the state of Utah as the site of experiment. The annual precipitation of this region isapproximately 250 mm and the rate of “good” weather is more than ∼ 60 % of the year.
The original air ﬂuorescence experiment, Fly’s Eye, operated in the vicinity and recorded
the measurement duty factor of 10 %. The second generation experiment, HiRes, hasmonitored the air clarity over one year, and concluded that the air clarity of this region inequivalent or better than the US standard desert model (see §3.3 for more details).
The deployment of TA measurement stations is shown in Fig. 2.1. A total of 10 stations
form an approximate two-dimensional array with the distance to the nearest neighbors 30–
45 km. A completely linear (one-dimensional) station deployment would give slightly larger
acceptance but the 2-dimensional array oﬀers a high level of redundancy by measuring thesame events with multiple number of stations. A minimum of 2 stations will be required
for the stereo reconstruction but more stations will give further information to check theinternal consistency of the energy and direction measurement. The level of consistency
is a good measure of the systematic uncertainty. The approximate sensitive area of theexperiment is shown by a set of circles in the ﬁgure. The Monte Carlo simulation shows
approximately 50,000 km str acceptance for 1020 eV protons.
The stations of HiRes experiment are located at the Camel’s Back and Five Mile Hills
in the Dugway Proving Ground (see Fig. 2.1). Its sensitive region overlaps with a northernedge of the TA’s acceptance. The ground array of the northern Pierre Auger Observatory
is indicated by the ‘Superman Triangle’ in the ﬁgure. Three stations of TA at Hell Hole,
Telegraph Point and AT&T are expected to serve as the ‘ﬂuorescence eye’ of the Auger
detector.
Table 2.1: List of TA sites.
#
1
2
3
4
5
6
7
8
9
10

location
Black RockHoneycomb
Drum Mountain
Foote Range
Chalk Knolls
Skull Rock Pass
Long Ridge
AT&T
Hell Hole
Telegraph Point

latitude39.873 N
39.724 N
39.610 N
39.460 N
39.300 N
39.031 N
39.151 N
39.074 N
39.081 N
38.880 N

longitude
113.258 W
113.583 W
113.167 W
113.822 W
113.533 W
113.340 W
113.070 W
112.842 W
112.536 W
112.639 W

The geographical locations of 10 candidate sites are listed in Table 2.1. All the stations
are at the altitude of 1500–1600 m above the sea level. Most of the land for the sites are
public lands owned by the Federal Government, and the permission of the use is to be
applied to the Bureau of Land Management. Some details of the site attributes are given
elsewhere [81]. The northern 5 stations (#1 – #5) and AT&T (#8) are located on a knoll ora small hill approximately 100 m above the surrounding land. It is favorable for having lessobscuration in the ﬁeld of view and for avoiding the coverage of the fog and the mist near

30

CHAPTER 2. TA DETECTOR

the ground level. Theses sites are remote and the construction of access road to the top of
the knoll is required. The night sky is very dark for these stations. Other stations, mainlyin the southern part of the TA acceptance, are on the small plateau and the elevation withrespect to the surrounding land is not large. The access is easier but the road and farming
land suggest a possible disturbance to the measurement by higher human activities. Thereis a large lake (Sevier Lake), a small town (Delta) and a power plant (Intermountain Power
Plant) in this region. Although these are no essential obstacles to the ﬁrst sight, we intend
to carefully investigate the diﬀerence of the night sky background and the atmosphericclarity between the northern and southern sites.

FIG. 2.2: Plan and cross sectional view of the telescope housing.
The site will be ﬂattened to install a station building shown in Fig. 2.2. The building
has a diameter of ∼ 30 m and the height of ∼ 10 m. A gravel road with the width of ∼15 feet will be made from the nearby public road to the site on top of the hill. The station
requires approximately 70 kWatt of electricity for the electronics, computers and associatedinstallations such as the air conditioning and the rolling door of the station building. It will
be supplied from the nearest power line. In case the available power line is far away fromthe station, we intend to install a local power generator. A Uninterrupted Power Supply(UPS) system and a small generator with limited capability will be installed for the safety
operation of the station for emergency cases when the power is interrupted.
The computer network connection to the TA site is indispensable; it will be used forthe real time data exchange for the intersite trigger and laser shooting, remote control
and monitoring of the data acquisition, collection of the acquired data from each station

2.3. THE TELESCOPE AND OPTICS

31

to the central station and for the general communication between stations. We plan toinstall a private optical ﬁber line to all the stations for the network connection. For someof the remote stations, however, the network by the microwave communication may be themore convenient alternative, though it requires a straight line of sight and the speed ofcommunication is slower. We are in the process of installing a microwave connection to
one of the planned site (Black Rock Hills) to check its performance in the ﬁeld use. A
backup communication with limited capability may be supplied by the satellite telephone
communication. The safety related operation of the station such as the power on/oﬀ andopening/closing the rolling door will be controllable both by the optical ﬁber connection
and the satellite telephone connection.

2.3

The Telescope and Optics

A TA station consists of 40 units of ﬁxed telescopes each covering a certain region of thesky. The ﬁeld of view (FOV) of one telescope unit is 18.0◦ in azimuth and 15.5◦ in elevation.
The upper ring composed of 20 telescope units covers the entire azimuthal angle and theelevation angle of 3◦ – 18.5◦ . The lower ring covers 18.5◦ – 34◦ in elevation.
We have employed a spherical mirror optics to obtain a wide FOV with reasonablefocusing power. The support and adjustment mechanism for the segmented mirror is also
simpler for the spherical mirror compared with the parabolic one. A ray tracing simulation
is made for the spherical mirror telescope with a planar imaging plane located near the
focal point. The result is shown in Fig. 2.3. Parallel light beam was injected every 4◦ inhorizontal and vertical directions and its image on the camera is plotted. The obscurationby the PMT camera is taken into account. The spot size of 30 mm in FWHM is obtainedin most of the FOV. It is suﬃciently small compared with the PMT dimension (61 mm
between two opposite edges of hexagon) and does not contribute much for determining theresolution of the telescope.
The telescope has a main dish with a diameter of 3.3 m which is composed of 18 hexagonal
shape segment mirrors (see Fig.2.4). The attachment angle of each mirror is adjustable intwo directions. The location of the central mirror is made empty and is reserved for the
optical alignment system and PMT calibration system. The detailed design parameters of
the telescope and the segment mirror is given in Table 2.2.
A design of the segment mirror is shown in Fig. 2.5. The mirror is made by 10.5 mm
thick Tempax glass (Schott corp.). A support disk of 150 mm diameter made by the samematerial is glued behind the mirror by 3M Dymax 840 glue. The disk is used to support
the segment mirror from the telescope frame.
The segment mirror is shaped by heating a planar glass on a ceramic mold plate in thetemperature controlled electric oven (see Fig. 2.6). Including the annealing, the production
process takes one day to make one mirror. We expect the speciﬁcation of the mirror isachieved without signiﬁcant polishing. The mirror surface is coated with 200 nm thickaluminum produced by the vacuum deposition. A hard protection surface of Al2O3 crystal
with thickness of 50 nm is then produced in the solution containing ammonium hydroxide,
tartaric acid and ethylene glycol. The reﬂectivity of the ﬁnished mirror is shown as afunction of wavelength in Fig. 2.7. The reﬂectivity greater than 88% is obtained between

CHAPTER 2. TA DETECTOR

32

Images

y

50

0

-50
-50

0

50

x

light intensity

30

20

10

0
-50

0

50

x

FIG. 2.3: Expected image of TA telescope unit.

2.3. THE TELESCOPE AND OPTICS

33

FIG. 2.4: Mechanical design of TA telescope.

SchottTempaxR=6067+-40
10t

Ceramic Disk
150 φ

660
30

FIG. 2.5: Design of the segment mirror.

CHAPTER 2. TA DETECTOR

34

Table 2.2: Design parameters of TA telescope.
Telescope
Diameter
Total Mirror Area
Focal Length
Mirror Optics
F.O.V.
Max. Wind velocity for Operation
Number of Segmented Mirrors
Segment Mirror
Shape and Dimension
Mirror Area
Radius of Curvature
Spot Size
Base Material
Mirror Coating
Surface Protection
Reﬂectivity
Weight

3.3 m
6.8 m22960 mmspherical
18◦ horizontal × 15.5◦ vertical
15 m/sec18
hexagonal, 660 mm between opposing edges
0.377 m2
6067 ± 40mm
≤ 10mm in diameter
Tempax glass, 10.5 mm thickaluminumanodization; Al2O3 , ∼ 50 nm≥ 88 % at 350 nm
10.7 kg

330 nm and 450 nm. This curve can be adjusted to have a peak around 350 nm by tuning
the thickness of anodization. The anodized surface is stable and the degradation of thereﬂectivity is ∼ 1 %/year from the experience of Fly’s Eye and Utah Seven Telescopes
groups. The mirror surface can be washed by pure water for the regular maintenance inthe ﬁeld.
We are simulating the distortion of the mirror system by the high velocity wind using
the ﬁnite element analysis. The displacement of the mirror is to be less than a few mm
under the wind velocity of 15 m/sec. Such a high speed wind occurs in less than 1 % of theobservation time according to the weather monitoring at Dugway Proving Ground, where
Fly’s Eye and Utah Seven telescope groups had been operated. The temperature coeﬃcientof the focal length was measured and found to be negligibly small (0.3 mm/degree).
Safety hazard tests were made for the prototype mirrors by destroying the mirror by
applying the impulsive shock at the edge of the mirror. The present design stands for theshock applied with a momentum of 250 kg m/sec, which corresponds to a kick or a straightpunch to the mirror by human adults.

2.3. THE TELESCOPE AND OPTICS

35

FIG. 2.6: Electric oven (left) and ceramic mold (right) used for the production of segment
mirror.

reflectance (%)

100

90

80

70

60

50
200

250

300

350

400

450

500

550

600

650

wave length (nm)FIG. 2.7: Mirror reﬂectivity as a function of wavelength measured after the anodization.

CHAPTER 2. TA DETECTOR

36

2.4

Photomultiplier and Camera

A set of 256 hexagonal PMTs is arranged in 16×16 array to form an imaging plane of thecamera. A single camera covers the sky of 18◦ in azimuth and 15.6◦ in elevation with a pixel
acceptance of 1.1◦ × 1.0◦ for one PMT. A UV transparent ﬁlter (BG3) with a thickness of 6
mm is placed in front of the PMT to reduce the number of night sky background photons.
A wedge-shaped reﬂector is installed at the edge of the photocathode to minimize theinsensitive area between PMTs and to improve the uniformity of the imaging plane. The
calibration and monitoring of the PMT gain will be made with a small light pulser of
YAP scintillator mounted on a computer controlled X-Y stage in front of the camera. The
electronic circuits including the digital processing units are installed inside the camera box,
so that the number of cables to the central station are much reduced.

2.4.1

PMT

PMT: Hamamatsu R6234
The PMT planned to be used in the Telescope Array project is Hamamatsu R6234, which
has a hexagonal bialkali photocathode and borosilicate glass window. The dimensions of
the PMT and a typical quantum eﬃciency are shown in Fig. 2.8. The PMT has 8 dynodesof a box-line focus type and a typical gain of 2.7 × 105 at 1000V. Characteristics of the
PMT are summarized in Table 2.3.
(b)quantum efficiency

(a)

0.3

0.25

0.2

0.15

0.1

0.05

0

300

350

400

450

500

550

600

650

700

wave length (nm)FIG. 2.8: (a) Dimensions of HamamatsuR6234. (b)Typical quantum eﬃciency of Hamamatsu R6234.

The bleeder circuits
The ﬁeld of view of one PMT (pixel) is about 1◦ . The night sky background is approximately 30 photoelectrons in 200 ns and it is equivalent to the anode current of 1.9μA at
the gain of 8 × 104 (see §2.5 for details). This is not completely negligible compared with

2.4. PHOTOMULTIPLIER AND CAMERA

K

37

G

P
DY1 DY2

DY3

DY4

DY5

DY6

DY7

C2

DY8

R2
2R

2R

R

R

R

R

R

R

C

r

r

z

z

C

C

C2
R=470kOhm
R2=100kOhm
R3=10kOhm

R3

C=10nF
C2=4.7nF
z=100V zener

GND

+HV

FIG. 2.9: Hybrid bleeder circuit with Zener diodes.

(a)relative gain

PMT gain
1.5
1.4
1.3
1.2
1.1
1
0.9
0

10

20

30

40

50

60

70

relative gain

(b)

80

90

100

anode current (μA)

1.5
1.4
1.3
1.2
1.1
1
0.9
0

20

40

60

80

100

120

140

anode current (μA)

FIG. 2.10: Pulse gain variation against background anode current, with the ordinary
bleeder circuit (a) and with the hybrid bleeder circuit (b).

CHAPTER 2. TA DETECTOR

38

Table 2.3: Characteristics of the Hamamatsu R6234
Shape and Dimension
hexagonal, 60 mm diagonal
Dynode Structure
box-line focus
Number of Dynodes
8
Quantum Eﬃciency (max.)
30 %Gain (typ.)2.7 × 105 (1000 V)
Anode Dark Current (typ.)
2 nA
Anode Dark Current (max.)
20 nA
Rise Time
6.0 nsTransit Time
52 ns

the maximum bleeder current of ∼ 0.2 mA. Moreover, the anode current ﬂuctuates continuously during the observations. This ﬂuctuation changes the PMT gain signiﬁcantly when
we use an ordinary bleeder circuit by the register chain. In order to avoid this problem,
we developed a hybrid bleeder circuit using Zener diodes at the last 2 stages of the dynode
chain (see Fig. 2.9).
The measured variation of the pulse gain against the background anode current is shownin Fig. 2.10. As shown in the ﬁgure, the pulse gain of the hybrid bleeder is almost constantin the wide range of anode currents.
Linearity
Following the simulation, the largest PMT signal to be detected is 6 × 104 photoelectronsin 200 ns time window (see §2.5 for detail). This corresponds to 4.2 mA anode current
assuming the PMT gain of 8 × 104 . The linearity of PMT depends on the relative voltages
applied to the last few dynodes. In Fig. 2.11 we show the linearity measured for the various
types of bleeder circuit. The hybrid bleeder with Zener diode shown in Fig. 2.9 (ﬁlled
circle) gives the optimum result. The deviation from the linear response is ∼ 1 % for theanode current of 4.2 mA, and is within 5 % up to 20 mA, which is suﬃcient for the TA’srequirement.
Temperature dependence
The PMT camera is exposed to the ambient air during the observation. The gain of
PMT may vary from hour to hour reﬂecting the temperature change of the PMT andbleeder circuit. It is necessary to measure the temperature dependence of the PMT pulse
gain and correct its eﬀect in the data analysis. We measured the PMT gain variation
for the ordinary and the hybrid bleeder circuit for a temperature range from −20◦ C to40◦ C. The results with the ordinary bleeder is shown in Fig. 2.12 (a). The temperaturecoeﬃcient is −0.39 ± 0.02 %/K and it is consistent with the typical temperature coeﬃcientof −0.2 ∼ −0.5 %/K for the bialkali PMT. The result of the same PMT with the hybrid
bleeder is shown in Fig. 2.12 (b), and the coeﬃcient is −0.57 ± 0.03 %/K. This result
is larger by 0.2 %/K than that of the ordinary bleeder, which can be explained by thetemperature coeﬃcient of Zener diodes (0.095 %/K in typical).

2.4. PHOTOMULTIPLIER AND CAMERA

39

FIG. 2.11: Measured linearity of the pulse gain for various bleeder circuits. All the measurements are made under the conditions of same pulse gain ∼ 105 (i.e., HV values are
diﬀerent). The light pulse width is 300ns. All the bleeders have the same registers until
DY6, as same as shown in Fig. 2.9. The resistances of (DY6–DY7),(DY7–DY8) and (DY8–P) are; open circle: R,2R,1.5R, open triangle: 2R,2R,2R. And the voltages of Zener diodesof (DY6–DY7),(DY7–DY8) and (DY8–P) are; filled triangle: 75V,130V,95V, open square:
62V,130V,100V, filled circle: R,100V,100V.

(a)

(b)

FIG. 2.12: (a) Measured temperature dependence of the relative PMT pulse gain for theordinary bleeder (a) and for the hybrid bleeder (b).

CHAPTER 2. TA DETECTOR

40
Optimization of the ﬁlter thickness

internal transmittance

(a)

(b)

1
0.9
0.8
0.7

SN ratio (arbitry unit)

We plan to use the optical ﬁlter, Schott BG3, passing photons only from 300 to 400 nm wave
length (see Fig. 2.13 (a)). Since the transmittance of the ﬁlter depends on the thickness,
we estimated its best thickness by referring to a signal to noise ratio (S/N).
90

85

80

0.6
0.5

75

0.4
0.3

70

0.2
0.1
65

0
200

250

300

350

400

450

500

550

600

650

wave length (nm)

0

1

2

3

4

5

6

7

8

9

10

filter thickness(mm)FIG. 2.13: (a) Internal transmittance of Schott BG3 ﬁlter of 1 mm thickness. (b) Signal
to noise ratio as a function of the ﬁlter thickness.
The calculated S/N is shown as a function of the ﬁlter thickness in Fig. 2.13 (b). The
S/N increases with the ﬁlter thickness, but is almost constant for the thickness more than
6 mm. We have chosen the ﬁlter thickness of 6 mm.
Uniformity of PMT cathodeThe sensitivity of the PMT has a position dependence on its photocathode surface, reﬂecting the non-uniformity of the quantum eﬃciency and the ampliﬁcation gain. Various
factors such as the photocathode thickness, the irregularity of the focusing electric ﬁelds
and the geometry of the ﬁrst few dynodes aﬀects the position dependence. We measured
the 2-dimensional response of the PMT by scanning the pulsed LED source on the PMT
window. The light source was mounted on a computer controlled XY stage. The spot size,
as well as its relative positioning accuracy, was ∼ 1mm. The measured anode gain map isshown in Fig. 2.14.
As we observe from the sensitivity map, there is ∼ 3 mm insensitive region at the edgeof the PMT glass envelope. Together with the physical gap between PMTs, it will form
an insensitive band of 7–8 mm at the boundary of the PMTs. We are in the process of
estimating the loss of ﬂuorescence light and the eﬀect on the event reconstruction by thesimulation. At the same time, we are designing a wedge-shaped reﬂector to be placedat the PMT boundary such that the ﬂuorescence light impinging on the insensitive bandis reﬂected and guided to the central region of the photocathode. This minimizes theinsensitive area and improves the uniformity of the imaging plane, thus minimizing thesystematic error.

2.4. PHOTOMULTIPLIER AND CAMERA

41

FIG. 2.14: Contour map of the measured anode gain (relative).

2.4.2

Calibration of PMT

YAP pulsar
We use YAP light pulsar (YAlO3 : Ce(YAP) + 241 Am) as the light sources for the PMT
calibration. The details of this light pulser are described in references [82, 83, 84, 85]. Its
luminous spectrum spans 300–400 nm (Fig. 2.15 (a)), and covers nicely the spectrum of air
ﬂuorescence. The structure and characteristics of the YAP pulsar (produced by Radiation
Instruments and New Components Ltd.) is shown in Fig. 2.15 (b) and described in Table
2.4, respectively.
Table 2.4: Characteristics of YAP pulsar
Diameter
5.0 ± 0.2mm
Thickness
1.2 ± 0.2mm
Pulse Frequency
58Hz
Pulse Height Distribution FWHM 5.5 %Peak Wave Length
370nm
UV LEDThe second light source is the UV LED (Nichia NSHU590E), whose characteristics aredescribed in Table 2.5. This light source has been used as a simulator of the night sky
background when we measured the characteristics of the PMT.
Table 2.5: Characteristics of UV LED (Nichia NSHU590E)
DC voltage
Emission Power
Peak Wave Length
FWHM of the Spectrum

3.9 V
750μW
370 nm
12 nm

CHAPTER 2. TA DETECTOR

42
(a)

(b)

FIG. 2.15: Spectrum and structure of YAP pulser.

2.4.3

Design of PMT Camera

The PMT camera is to be made as a closed box to avoid the PMT and electronics bedamages by the sand and dust of the environment. In addition, the ambient temperature
varies from −10 to 40◦ C, and the electronics inside the camera box is a heat source of 1.7
kW (estimated with a safety factor of 2, see Table 2.6 for detail). To cope with this problem
and guarantee a stable operation of the camera, it is imperative to equip the temperature
control system inside the camera box.
Table 2.6: Power consumption in a PMT camera box. The values are measured for the
prototype circuits.
parts
CSI-hybrid
ADC+DSP
Main
Front-end circuit
HV distributor

power
1.75 W/ch
0.75 W/ch
5 W/16ch
720 W/256ch
120 W/256ch

The overall design of the PMT camera is shown in Fig. 2.16. Each PMT is inserted
to an accurately machined hole of the aluminum support plate and ﬁxed with 4 screws
as shown in Fig. 2.17. The front of the camera is covered with an optical ﬁlter, Schott
BG3, attached to the frame, which can be opened for the access to the PMT for the
maintenance. A computer controlled XY scanning stage is attached to the ﬁlter frame
carrying the YAP pulser for the calibration of PMT and electronics. The back of the PMT
is covered by two doors, to which VME crates for the main digitizer/trigger board and
HV distributors are installed. The inner wall of the box is covered with heat insulators.

2.4. PHOTOMULTIPLIER AND CAMERA

43

A small air conditioning unit is installed inside the box for cooling the electronics. The
outer dimension of the box is 1300 mm × 1150 mm × 905 mm and the total weight of thecamera including the PMTs and the electronics circuits is about 250 kg. Since most of thedigitizer and trigger electronics are installed inside the camera box, the number of cables
coming out from the camera is much reduced, and only a few optical ﬁber cables and power
supply cables are to be connected to the camera box.
(a)

(b)
Z
Y
111
10

hood 55-Z

384
1000

X
30
10.June.1999

483?

S.Ogio200?

Tokyo Inst. Tech.
440?

495

495

W

FIG. 2.16: (a) PMT camera. (b) Plan view of the camera box. The dimensions are in mm.
(b)
34.6

(a)
133

34.6

117

20
6

10

PMT

52.83

61

16

44

55

52

CAB

10

60

55

CAB

30.5

filter30.5

61
7.July.1999

S.OgioTokyo Inst. Tech.

10.July.1999

S.Ogio52

Tokyo Inst. Tech.

FIG. 2.17: (a) Side view of the PMT and the supporting plate. (b) Front view of the
support plate.

CHAPTER 2. TA DETECTOR

44

PMT
o
FOV 1

Larger Npe
Smaller Npe
Longer Transit Time

Shorter Transit Time

100EeVpulse height[pe]5MHz Sampling

100

Gate for Trigger

50

0
5000

10000

time [nsec]

pulse height[pe]40100EeV
5MHz Sampling

Gate for Trigger
30
20
10
0
5000

10000

15000

20000

time [nsec]
FIG. 2.18: Typical PMT signals for diﬀerent event geometry.

2.5. ELECTRONICS AND TRIGGER

45

2.5

Electronics and Trigger

2.5.1

System requirement and overview

The strength and duration of the air-ﬂuorescence pulse depends largely on the geometry of
the event, as illustrated in Fig. 2.18. A well deﬁned short pulse with high amplitude will be
produced by the nearby air shower traversing the telescope’s line of sight perpendicularly.
A signal from the distant event with running away conﬁguration, on the other hand, will
be widely spread and is diﬃcult to be separated from the night sky background. The
recording of the signal time proﬁle becomes increasingly important for events with a long
duration, for which most of the information to determine the geometry (particularly the
direction) is included in the time information. Therefore the continuous digitization andrecording of the signal wave form is much preferred compared to the analog integration of
the signal with a ﬁxed gate width, or a ﬁxed time constant.

9
8
7
6
5
4
3
2
1
0

Td(μs)

Log10 (Npe/200ns)

Proton 1021eV

-100

0

100
Rp(km)

80
70
60
50
40
30
20
10
0
-10

-100

0

100
Rp(km)

FIG. 2.19: Maximum number of photoelectrons per 200 ns time bin for one PMT versus
impact parameter RP of the event (left). Signal duration versus RP for the same PMT(right).
We performed a Monte Carlo study to estimate a required dynamic range of the electronics. In Fig. 2.19, we show scatter plots of the maximum number of photoelectronscontained in 200 ns gate time v.s. its impact parameter for the 1021 eV proton air-shower
events. The rate of events in which at least one of the PMTs exceeded the ADC dynamic
range of 12 bits (16 bits) is roughly 30% (10%) assuming a LSB of digitization is taken
equal to one photoelectron in 200 ns. The diﬀerence between 12 bits and 16 bits increases
as we tighten the event selection cut. If we require more than 10 PMT hits with morethan 2 σ signiﬁcance level above the background, the overﬂow rates are 12% and 58% for
16-bit and 12-bit dynamic range respectively. This concludes the dynamic range of 16 bits
is needed for the ADC system to be unsaturated up to 1021 eV event. The requirement
can be alleviated if we take a LSB sensitivity to be at signiﬁcantly lower level, say at thelevel of the night sky background (∼30 photoelectrons in 200 ns). But the monitoring of

46

CHAPTER 2. TA DETECTOR

the background level will be unreliable for such a system, and a signal separation from thebackground will be much deteriorated for the online and oﬄine analysis.
The duration of the signal for the PMT with the highest number of photoelectrons isplotted in Fig. 2.19 against the impact parameter of the event. It indicates some events
can generate ﬂuorescence signal as long as 70 μs. An elaborate and ﬂexible algorithm will
be required online and oﬄine to identify a signal and maximize the signal to noise ratio(S/N). We checked that the 25.6 μs time window is practically suﬃcient for the signal
ﬁnding for the triggering purpose. The necessary time depth for the event recording canbe determined for each event by the DSP software.
A good S/N will allow us to trigger and analyzed lower energy events. Given D=1.6m,
d=14cm, and S/N=4 for Fly’s Eye and D=3m, d=6cm, and S/N=2 for TA, we will be able
to decrease the threshold energy for detection down to 1016 eV, which is about an order ofmagnitude smaller than that of Fly’s Eye. Here the D is a mirror diameter and d is a PMT
diameter. This would allow us to study cosmic rays in this energy region and speciﬁcally
opens up a possibility of detecting the neutrinos from AGN.
Monte Carlo studies indicate that many showers that trigger one station will also be seen
by several neighboring stations. Even if the neighboring telescope does not see enough of
the light to trigger on that shower, there will be information present useful for the stereo
reconstruction of the event. The system of broadcasting triggers seen by one detector to
its neighboring detectors will be thus important. When a trigger occurs in one detector,
the data of its neighboring detectors will be examined and any hits found will be written
into the data stream.

FIG. 2.20: Block diagram of the TA online system.

2.5. ELECTRONICS AND TRIGGER

47

A baseline design of the TA signal digitization, trigger and data acquisition was drawn
to satisfy above conditions (see Fig. 2.20). Its main features are summarized below;(1) AD conversion with 12-bit resolution and 50 MHz continuous sampling using apipelined ADC chip.
(2) 16-bit dynamic range using H/L 2-range scheme at the front-end charge sampling
LSI (custom development). Here LSB sensitivity is taken equal to one photoelectronin 200 ns time window.
(3) on-ﬂight software recognition of ﬂuorescence signal by the DSP attached to eachchannel.
(4) generation of trigger in 3-dimensional space; XY (camera) coordinates and T (time)
coordinate by software.
(5) exchange of trigger information between stations (intersite trigger).
In Chapter 4, we present the expected performance of TA obtained by the Monte Carlosimulation, and items (1)–(3) above have been taken into account in this simulation.

2.5.2

Front-end Electronics System

The front-end electronics for TA is one of the most critical elements to achieve a large
aperture of the detector and lower threshold of cosmic ray primary energy. In the pioneering
work of the Fly’s Eye detector, analog sample-and-hold circuit with a slow AD converter[86] was adopted. In the subsequent HiRes detector, 8-bit ﬂash ADC was introduced withadditional analog sum measurements to circumvent the eﬀect of over range [87].
A new pipelined ADC technology and a wide spread of digital video system enable us to
use a fast and wide dynamic range ADC for all channels. The pipelined ADC is fabricatedin a CMOS process, and it has superi or characteristics of low power, low cost and highspeed. A 12-bit 5-MHz sample ADC is commercially available in less than $7.
While the fast ADC system could give us more information on air shower, it increases
data size almost 100 times. Thus a large bandwidth is required in data acquisition system.
Furthermore, to maximize the merit of the fast digitization, it is indispensable to process
the data in real time to increase signal to noise ratio. This is particularly important in
the ﬂuorescence measurement since the signal wave form varies greatly depending on thezenith angle and the impact parameter.
To process the digital data in real time, a large processing power is required. Fortunately,
recent progress in digital products introduces high-performance, low-cost Digital Signal
Processors (DSPs). There are several DSPs, performances of which are more than 100
MIPS and the price is about $6. By using these DSPs we will be able to search optimal
signal width for ﬂuorescence signal in real time.

CHAPTER 2. TA DETECTOR

48(a) Charge amp

from
PMT

Bias Voltage

to ADC(b) Charge Successive
Integrator
Integrate

Read

Reset
from
PMT
to ADC

Charge Integration Methods
FIG. 2.21: Schematics of Charge Successive Integrator.
Charge Integration
A charge integration method is essential in designing a calorimetricmeasurement. To
98.12.18 Y.A.
implement the baseline design, we are developing a Charge Successive Integrator (CSI) LSI.
(Fig. 2.21). It has 3 rotating capacitances which serves for the integration, signal output
to ADC, and reset successively for each 200 ns. Required signal range for the CSI (andPMT) is summarized in the following lists. Here we assume a PMT ampliﬁcation of 8 ×
104 and 20 pF storage capacitance for the CSI. The LSB in the low range (a unity gain
before CSI) corresponds to 1 photoelectron in 200 ns. The maximum signal corresponds
to 65,536 (=216 ) photoelectrons in 200 ns and is detected in the high range (a gain of 1/16
before CSI).
– Least count sensitivity: A 10 ns wide (square) pulse from PMT has a (peak)current of 1.28 μA and a total charge of 13 fC. This is equivalent to 0.6 mV of stored
voltage on the CSI capacitance (low range used).
– Full scale sensitivity: 65,536 photoelectrons in 200 ns corresponds to 4.2 mAcurrent from PMT for the same duration. The total charge from PMT is 840 pC andthis becomes 2.6 V on the CSI capacitance (high range used).

2.5. ELECTRONICS AND TRIGGER

49

FIG. 2.22: Layout of the test CSI cell designed in 0.6 μm CMOS technology. In thisparticular cell, 12 pF integration capacitors were used.

CSI (Charge Successive Integrator)
SRdataIntegrator
OPAMP

DAC(10bit)

Shift
Register

DAC(10bit)

AMP̲VthIntegrator
12

Integrator
Vthx1
Integrator

Analog Signal x16

OUT
VGA

Integrator
Integrator
1/16

Integrator
Integrator

High/Low Signal
Comparator

reset
CLK
SData
SCLK

RotatorSData
DAC(8bit)Vth

FIG. 2.23: Schematic of the CSI with two-range scheme.

Vth̲monCHAPTER 2. TA DETECTOR

50– Night sky background: We assume 30 photoelectrons in 200 ns. This is equivalent
to a continuous current of 1.9 μA from PMT and 19 mV stored on the CSI capacitance(low range used).
The CSI will be fabricated in a CMOS technology. In this technology the value of thecapacitor matches in 0.1% level, and no correction will be necessary. But the area of CSIVLSI limits the integration capacitance less than ∼200 pF. A test CSI chip using a 0.6 μm
single-poly, triple-metal CMOS process was fabricated (Fig. 2.22) at Rohm Co. through
VLSI Design and Education Center (VDEC, Univ. of Tokyo) multi project ware service.
While the prototype CSI chip includes only one range of circuit, ﬁnal chip will implement
2-range scheme as shown in Fig. 2.23.
Pipelined ADC
Recent progress in digital video system brings a new high-speed, large dynamic-range, lowpower, low-cost ADC. Technique used here is called pipelined ADC (Fig. 2.24). The ADC
has many pipelined stages, and digitization of only one or two bit is done at each stage.
This ADC is fabricated in similar process used in CMOS digital LSIs and there are very
little analog elements in the chip. A digital error correction technique is usually employedto achieve a high precision.
We are presently using Burr-Brown ADS803 and its power consumption is only 115 mW.
The ADC has 12-bit dynamic range and 5 MHz-conversion rate.

-

V(i)

+

V(i+1)= 2V(i) ± Vref

+Vref -Vref

V(in)stage 1stage 2

register+stage n-1

register+stage nregister+Word

Calibration Control / Correction Logic

FIG. 2.24: Pipelined ADC.
DSPThe ADC converts a PMT signal continuously at 5 MHz frequency, and 12-bit data together
with additional information such as a range and an overﬂow bit are successively stored into

2.5. ELECTRONICS AND TRIGGER

51

ADC value

the memory of dedicated DSP. A high-performance DSP is needed to run a signal ﬁnding
algorithm in real time on the stored data. We are presently using a TMS320C549 DSP from
Texas Instruments. This DSP runs at 100 MHz, and many operations can be performed
in one cycle. The C549 has 3 internal data bus and one program bus, and consists of 6
stage pipelines. It contains 32k word internal memory that is enough for our application.
The DSP consumes only 100 mW/chip. Since the ADC generates 12-bit data every 200
ns, there are 20 cycles for one data in average. We set 25.6 μs time window for ﬁnding asignal. Since this window has 8.5 μs overlap with the next window, a total of ∼1,700 DSP
cycles (17.1 μs) can be executed for 128 data words (25.6 μs) to identify the ﬂuorescencesignal.
An example of signal ﬁnding algorithm at DSP is illustrated in Fig.√2.25. The program
looks for a set of signal edges T1 and T2 which maximize the S/N or Q/ BG. According toa Monte Carlo study, the charge resolution by this algorithm is 50 % for 10 photoelectrons(Q=10) and 20 % for 50 photoelectrons.

25.6 micro sec
Search Window
T1

T2

Q
BG Average

BG
S/N(T1,T2) =

Time

Q
1/2

BG

FIG. 2.25: Signal ﬁnding algorithm.

2.5.3

Signal Finder Module

A Signal Finder Module, which contains the front-end CSI, ADC and DSP, has been
prototyped (see Fig. 2.26 and 2.27). The schematics of the module is shown in Fig. 2.28.
The module is implemented in a 6U VME board and contains 16 channels. The gain andoﬀset of each channel can be corrected before the CSI with 16-bit DAC. The single range
hybrid version of CSI is used for the present prototype and it will be replaced by the 2-range
LSI version in future.
Data transfer between the ADC and the DSP internal memory will be done throughan 8-bit host port interface of the DSP with a maximum speed of 20MB/s. ADC data
are automatically transferred to internal circular buﬀer without DSP intervention (seeFig. 2.29). The size of the circular memory is 2k words, thus the data can be stored in thememory up to 400 μs (200 ns ×2 kW). For the intersite trigger which requires a longer
latency than 400 μs, a data copy operation is required to the external memory.

CHAPTER 2. TA DETECTOR

52

FIG. 2.26: Prototype signal ﬁnder sub-board for one channel.

FIG. 2.27: Prototype for the main module of signal ﬁnder. The height of the module is 6U
but the depth of the module is extended to 26 cm.

ADS803(5MHz)
12
A
16
D
Buf
C O.F. sw
3

CSI
Ch0

gain
offsetC549 DSP
DSP core
100 MIPS
I/O

32kW
RAM

10MHz
Clock

VME I/F
CPLD

Dual Port Mem
(8kB)

Ch1

•
•
16ch
•

5MHz
System
Clock

V
M
E
B
U
S

Flash Mem(256kB)

Ch15
C549
DSP
TriggerModule

RS422

Serial Line

UART

:

16bit D/A
(x 2)

Control
CPLD

JTAG

AnalogPower

FIG. 2.28: Block diagram of the 16-ch prototype Signal Finder module. The module is
implemented in a 6U VME board.

2.6. INTERSITE TRIGGER SYSTEM

LVDS

53

Host Port I/F
Data latch

Data

DSP Memory

12
8

MUX
16

5MHz
ADC

Address reg.

Data
MUX

11

Overflow
Cycle
Count

HPI Memory(2KW)
Circular Buffer

Address3

DSP core
Analog side

Digital sideC54x DSP

FIG. 2.29: ADC to DSP interface.
Between the ADC and the host port, 12-bit data and an overﬂow bit are transferred. In
addition, 2 bits are transferred to a 2-bit counter, which is used to check the data sequence.
Last one bit is reserved for data ﬂow control which is used in DSP software. This is realized
by two 8-bit data transfer cycles. In order to avoid the interference of the digital signal
to the sensitive analog circuit, LVDS (Low Voltage Diﬀerential Signaling) drivers/receivers
are used for the digital signal transfer.
All the individual DSPs are controlled by another DSP, which collects the processed
information (T1, T2, Q and S/N, etc.), and send them to the trigger module through its
serial lines at 50 Mbps. An easy-to-use commercial PC tool can be connected to the module
via JTAG boundary scan port for debugging and monitoring of the DSPs. A dual port
memory of 8 kB is used to exchange the data between the module and a VME mastermodule. A Flash memory of 256 kB is included to store program and parameters. The
whole system can be synchronized by using an external system clock of 5 MHz.

2.6

Intersite Trigger System

A schematics of the intersite trigger system, being implemented as the radio link between
a pair of HiRes stations, is shown in Fig. 2.30. In this diagram information ﬂows from left
to right. After a trigger is formed, the information to be sent to neighboring detectors is
encoded in an interface card, passed to the radio transmitter, and sent to the mountain
where the neighboring detector is located. At that site the information is decoded by asecond interface card and passed to the ﬂash ADC readout system so the data there canbe examined for hits from the triggering shower. This ﬁgure shows a single, one-way radioCHAPTER 2. TA DETECTOR

54@

Interface

Interface

@
Q @
Q
PPQ@
PQ
P


 




Antennas@

Transmitter@ext. trig.

ReceiverSite 2FADC Electronics

Site 1 Mirrors
Triggering Detector

Neighboring Detector

FIG. 2.30: Block diagram of intersite trigger
channel, but the radios we will use for TA will be two-way, with separate frequencies, transmitters, and receivers for each direction. Each element of the intersite trigger, connecting
two sites, will cost about $22,000.
The information passed between two HiRes sites consists of a signal at the time of thetrigger plus a 5-bit word which is the number of the triggering mirror. The Telescope
Array data-collection system will allow us to transmit more information for the intersite
trigger. We feel that the most useful information will be the length of the track seen at thetriggering site. Having this information will allow the neighboring site to grade triggers
and, if the data rate is momentarily high, only pick the most interesting intersite triggers
to act upon.
We intend to connect all TA stations by the optical ﬁber network. One of the important
purposes of the ﬁber link is to use it for the intersite trigger. We continue to study opticalﬁber and radio communications for the intersite trigger.

2.7

Data acquisition and online system

2.7.1

Data acquisition

An event size distribution of one TA station for the air shower events with energies above
1019 eV is shown in Fig. 2.31. The size is less than 1.5 kB for 90 % of the event. The
event rate of air shower with energy more than 1016 eV is less than 0.3 Hz per station.
Even we assume a maximum trigger rate of 10 Hz caused by the Cherenkov light of low
energy showers and muons, the maximum data transfer rate is 15 kB/s. This rate of event
building can be comfortably achieved by the Ethernet technology.
An overall scheme of TA event building is shown in Fig. 2.32. Once the signal ﬁnder
module receives a DAQ request from the trigger, the stored data in the internal memory of2.7. DATA ACQUISITION AND ONLINE SYSTEM

55

Frequency (Arbitrary Unit)

40

30

20

10

0
0

500

1000

1500

2000

Data Size [Bytes]

FIG. 2.31: Data size for air shower event.
SW HUBVME Crate
16ch x 16

PC
NIC

SW HUB
WAN(InterStation)
PC
NIC

Adapter
Adapter
Adapter

NIC

Adapter

16ch x 16

NIC

NIC

PC

x 20 segments / 1 Station

FIG. 2.32: TA data acquisition system.

PC
NIC

NIC

PC

HD
DVD-RW
Tape

CHAPTER 2. TA DETECTOR

56

DSP are sent to the event builder computer through a VME bus and VME/PCI adapter.
Data from 512 channels (two telescopes) are gathered into one VME crate consisting of 8
units of 64ch signal ﬁnder modules and 1 VME/PCI adapter card. The adapter will send
the combined data into 1 front-end network PC. The switching HUB is to merge the fastethernet data packets from 20 network PCs into the event builder PC by Giga-bit ethernet
technique. An additional 2 PCs connected by the Giga-bit ethernet LAN will form a DAQ
computing farm. The DAQ farm is responsible for the event building, ﬁltering, quick online
analysis and monitoring, and the maintenance of online calibration database.

2.7.2

Slow Control

In addition to the data acquisition function, the online system will be responsible for theslow control function such as;(1) gain calibration of electronics.
(2) high-voltage monitor and control.
(3) atmospheric monitor.
(4) environmental supervising.

2.7.3

Structure of online software

The TA data acquisition (DAQ) system should handle 10,240 signal channels at each station. To increase the data taking eﬃciency and the data quality, a DAQ system with highdegrees of homogeneity, ﬂexibility and scalability is required. We are now building ourown DAQ system by modifying CASCADE DAQ system [88], a multi-processor real-timedata-acquisition system for High Energy Physics (HEP) experiments developed at CERN
by the ECP-DS group.
The concept of a unit construction system has been followed. The basic software unit,
called the stage, and the stage connection unit, called the inter-stage link, have been deﬁned.
Plugs for special-purpose connections like event monitoring, run control and experiment
speciﬁc functions are provided. This approach allows for easy task distribution and theircommunications in a distributed system using a variety of operating system and physicalhardware connections.
The stage is the fundamental construction of the DAQ system. It performs the basic
functionality of a general single-processor, single-process, data-acquisition kernel. It is
structured and parameterized so that several stages can be grouped together to form subsystems such as event builders or farms.
The stage is organized to perform several threads of execution. This allows operations
to take place concurrently on diﬀerent events so that the stage can deal with a number of
input and output ports at their individual rates. The thread scheduling sequence in thestage is performed on a priority basis and has no ﬁxed sequence. This is opposed to theﬂow of a particular event through a stage, which passes from one thread to the next in a

2.7. DATA ACQUISITION AND ONLINE SYSTEM

57

well deﬁned order. Each thread corresponds to a given operation to be performed on an
event or to a control action to be done on the stage.
Two consecutive stage units in the data-ﬂow topology are linked by the DAQ connection
unit, the inter-stage link. Communication between two stages is initiated by the dispatch
phase of the upstream stage, which triggers the input phase of the downstream stage bysending it a signal. The protocol includes exchange of a message containing the event
descriptor followed by the transfer of the event data. An acknowledge message is sent by
the downstream stage to the link-acknowledge phase of the upstream phase once the event
has been successfully transferred.
A high-level interface and a handshake protocol has been speciﬁed for the inter-stage
link communication. They have been implemented on a number of hardware and software
platforms.

2.7.4

Run Control

The run control facility is comprised of two processes running on a UNIX PC: the runcontrol engine (NRC) and the human interface (XHI). NRC is a modular, general-purpose
control program allowing complex data-acquisition systems to be modeled in an objectoriented way. It is based on a system originally designed by the OPAL [89] experiment andadapted in collaboration with NOMAD to better suit their needs. Operator interaction
with the data-acquisition system is achieved by XHI, an X11/Motif program which provides
a run time conﬁgurable graphical interface including menus, dialog boxes and various typesof display panels.
NRC is a process controlling DAQ units such as stages, recorders, monitoring programs
and user speciﬁc processes. Its main purpose is to provide synchronization between various
DAQ units and to hold their respective states. Within NRC, each element is described ina uniform way as a Finite State Machine (FSM). A FSM is an object having a predeﬁned
set of allowed states and allowed transitions between these states. Since DAQ units are
external to NRC, they are represented by internal FSM correspondents. A hierarchy ofinternal FSMs can be introduced to control subsets of the entire DAQ system.
Communication between NRC and the external FSMs is based on NIC, the TA Network
component package via TCP/IP. The XHI, although a special object, communicates with
NRC in the same way as the DAQ units. The NRC master is the network server and theexternal DAQ units are the clients, which can connect dynamically to the server. NRC
maintains the states of all the data acquisition components as well as run time parametersin an external ORACLE data base. A run control domain is deﬁned by an identiﬁer which
is used by NRC and the connected FSM’s. In a given domain each object is identiﬁedby its unique ASCII name. More than one instance of the run control facility may berunning at a given time using diﬀerent addressing domains. For example a full production
run can coexist with the test or calibration of a particular sub-system. When the NRC
program is stated, the conﬁguration information is read from an ORACLE data base. This
information is used to build the run control data structures: the FSM deﬁnitions, default
state of objects, state transitions, elements of the graphical user interface and run timeparameters. A NRC user library allows for easy preparation of an external DAQ unit using
three function calls.

CHAPTER 2. TA DETECTOR

58

2.8

ComputingComputing facility is used for a data management, physical/technical analysis, simulation
work and any related computing tasks necessary for the TA experiment. This facility has
to furnish enough ability for computing and data storage to all researchers, engineers andstudents in TA experiment working on-site and at each collaborating institute in Australia,
Japan and USA through an established network.

1111111111111
0000000000000
0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111
Application Server
0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111

DATA
Storage111111111
000000000
000000000
111111111
Mail Server
000000000
111111111
000000000
111111111
111111111
000000000
000000000
111111111
FTP server
000000000
111111111
000000000
111111111
000000000
111111111
Multimedia
000000000
111111111
Server000000000
111111111
000000000
111111111

Data Processing Center

1111111111111
0000000000000
0000000000000
1111111111111
0000000000000
1111111111111
Data Processing
0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111
Server0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111
0000000000000
1111111111111
111111111111
000000000000
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111
Front End Server
000000000000
111111111111
000000000000
111111111111
000000000000
111111111111

WWW
TA Network

111111000000000000111111000000111111000000111111000000111111000000111111
User
User
User
000000111111000000111111000000111111

Internet

Local Network

FIG. 2.33: Computing service of TA experiment.
A conceptual design of TA computing facility is shown in Fig. 2.33. It consists of two
major servers; Data Processing Server and Application Server. The Data Processing
Server consists of 8 work stations equipped with 667 MHz Alpha-21264 (dual processors)
and unix based operation system. It is for a basic analysis of experimental data andsimulation studies oriented for heavy CPU time load. This frame has 2000 GB hard disk
system for the permanent data storage and temporary use. Also 5 Digital Linear Tape
(DLT) drives are attached to the server for an additional on-line data storage and backup
system. The Application Server is dedicated to the analysis of individual physical andtechnical problems oriented more for the I/O load and human interactivity. The analysis
of atmospheric calibration data is an example of this. This server also consists of 10 work
stations same with Data Processing Server, 4000 GB user disk area and 5 DLT drives.
The Front End Server is placed between two major servers and the user. It manages
a user authorization and system related management/service tasks for the convenience of
all the users. In addition, it will play an important role for the communication between
the TA collaborators by oﬀering a common notice board and Web-site services. Additional

2.8. COMPUTING

59

servers for mail, FTP and a Multimedia will be installed in the system. A total of 15
terminal stations will be available for the local user of the facility.
For the system stability and safety, a UPS system with high capacity battery and a
voltage stabilizer is installed in the AC power line. In case of a sudden power failure,
all equipment will be shut down with a proper procedure before the ensuring time of 20
minutes expires. Computing and network system has to provide a high quality and reliable
performance to carry out the experiment smoothly and to support user activity. Present
design meets such demands on its ability, convenience and reliability.

Chapter 3
Atmospheric monitoring
3.1

Overview

The understanding of the atmosphere is essential to the air ﬂuorescence technique of measuring particles with energies from 1017 eV to 1020 eV and beyond. The atmosphere isrequired for the primary particle to interact, the subsequent shower to develop, and theforward going Cherenkov light and isotropic ultra-violet (UV) light to be produced. Detailsof the UV light production yield details of the primary particle. The amount of UV light
produced is proportional to the particle’s energy. The shape and atmospheric depth of theshower proﬁle contain information about the composition of the primary particle.
However, once the light is produced, the amount that reaches the optical detectors depends on how the light propagates between the shower and the detector. If the atmosphere
were to somehow disappear just after the light was produced, the fraction of light reaching the detector would be a simple function of shower and detector geometry. Of course
the atmosphere is always present; the beneﬁt of light production that make experiments
such as Fly’s Eye, HiRes, and the Telescope Array possible is balanced by the challenge
to understand the light propagation. The challenge increases for the next generation ofexperiments that plan to explore higher energies because the most interesting showers will
be farther away from the detectors. For example, while the overall size of TA is larger than
HiRes, the 10–30 km distances at which HiRes observes high energy events overlaps withthe expected 20–40 km detector/shower separation expected for TA.
In order to maximize the performance, the TA experiment will be located in the same dry
clear desert where relatively few aerosols are present. The west Utah desert has some of theclearest air in the world. Secondly the detector stations will be built on hills several hundred
meters above the desert ﬂoor so that the optical detectors are above much of the ground
fog and local dust. Finally, the experiment will include systems to monitor atmosphericclarity locally and throughout the detector aperture while the detector is collecting data.
These systems will include artiﬁcial light sources, primary lasers, that ﬁre beams of photons
throughout the detector aperture. The same array of detectors that measure light fromair showers also measure the scattered light from the artiﬁcial light sources. Changes inatmospheric clarity will change the amount of light observed from both the artiﬁcial lightsources and the air showers. In this experiment, we anticipate that the techniques used at
HiRes will also work for TA.
61

CHAPTER 3. ATMOSPHERIC MONITORING

62

Continuing joint US and Japanese R&D eﬀorts in atmospheric monitoring will enhance
the tools available by providing independent cross checks and additional constraints. ThisR&D eﬀort continues to evaluate other techniques including back-scatter LIDAR systems
and systems to directly measure the horizontal attenuation.
20

Height(km)TA Field of View
15

Ring 2

10

5

Ring 1

0
0

10

20

30

40

Distance(km)FIG. 3.1: Field of View in Height vs Distance for Telescope Array. The aperture of theTelescope Array detector (TA) extends approximately 30–40 km horizontally and 10 km
vertically from the two detector stations. This ﬁeld of view is similar to that of the HiRes
experiment.

3.2

Components of the Atmosphere

For the purposes of an air ﬂuorescence experiment, the atmosphere may be considered tohave two parts: molecular and aerosol. The molecular component consists of the oxygen/nitrogen mixture. Although the density proﬁle verses height varies slightly between
winter and summer, the molecular component bounds the problem by providing the clearest, best-case, viewing conditions. The aerosol component consists of everything else suchas dust, pollution, fog, clouds. This component is not constant, varying with time andlocation.
The molecular and aerosol components scatter the Cherenkov and scintillation light.
There is also a third component, ozone, that absorbs light but its eﬀects are negligible
at the wavelengths of interest. The scintillation light produced by air showers falls in the
300–400 nm wavelength range [90] , just below the blue end of the visible spectrum.
The heart of the atmospheric monitoring problem for air ﬂuorescent experiments is tomonitor the distribution of aerosols in the detector aperture when data is being collected
and to understand how light propagates through them. Speciﬁcally, one needs to know twoquantities.
– The transmission coeﬃcient between the shower and the detector is required to determine the shower energy and proﬁle from the measured signals.

3.2. COMPONENTS OF THE ATMOSPHERE63– The scattering probability as a function of scattering angle is needed understand theamount of scattered cherenkov light reaching the detector to that it can be subtracted
from the ﬂuorescence part of the signal.
These quantities can be extracted from measurements of laser and “ﬂasher” shots ﬁred
through the detector aperture. Two approaches are possible. One uses select geometries todeconvolve the eﬀects of aerosol scattering and extract the transmission. The second ﬁts anaerosol model to the observed data to determine the model parameters. These parameters
include a horizontal attenuation length, an aerosol scale height, and a scattering dependenceor phase function.

3.2.1

The Molecular Component

The molecular part can be described analytically by the Rayleigh scattering theory. In thistreatment, the nitrogen and oxygen molecules are treated as dielectric spheres that are muchsmaller than the wavelength of the incident light. This theory has several consequencesthat are important to ﬂuorescence experiments. The probability for scattering increases
rapidly as the wavelength decreases, proportional to 1/λ4 . For more distant showers, thelonger wavelength end of the spectrum, i.e., the 391 nm line, will be enhanced relative tothe shorter wavelengths, i.e., the 337 nm line. The amount of light scattered at diﬀerent
angles varies by only a factor of two and is forward/backward symmetric, proportional to1+cos2 θ.

FIG. 3.2: Measurements by the USTA steerable telescope at Cedar Mt. The distributions
show the eﬀects of diﬀerent polarizations from the HiRes steerable laser 20 km distant.
Molecular scattering eﬀects have been observed by HiRes [91] and by the Cedar Mt
Telescope [92] by measuring scattered light from linearity polarized laser beams. Figure 3.2
shows these measurements for a set of shots measured by the USTA telescope at Cedar Mt
for two orthogonal linear polarizations and circularity polarized light. For this measurement
the beam was ﬁred nearly horizontally from the Camel’s Back site 20 km distant. Except forsmall scattering angles where aerosols diminate, the observed phase function is in agreement

64

CHAPTER 3. ATMOSPHERIC MONITORING

(a)

(b)

FIG. 3.3: Measurements of laser light at orthogonal linear polarizations and the ratio
between them. Molecular scattering theory predicts that the ratio should be cos2 θ. These
measurements were collected by the HiRes1 detector on relatively clear (a) and hazy (b)night.
with prediction for the Rayleigh scattering. The Rayleigh scattering theory also predicts
that the ratio of the amount of light scattered from a beam polarized in the scattering planeto the amount of light scattered from a beam polarized perpendicular to the scattering
plane will be cos2 θ where θ is the scattering angle. Using the HiRes1 detector as a receiver,results for a relatively aerosol-free night (Fig. 3.3 (a)) are in good agreement with the cos2 θ
prediction. This agreement lessens on a hazy night due to depolarization of the beam byaerosols (Fig. 3.3 (b)).
The density proﬁle of the molecular atmosphere and can be described by density andpressure at sea level and a scale height of 7.5 km. Daily and seasonal variations cause
small variations at the 5 % level. A more accurate description can be obtained by daily
radiosonde data in which pressure and temperature are recorded as a function of height byballoon based equipment released daily from major airports. Radiosonde data from Salt
Lake City Utah and Reno Nevada, were compared over the period of a year. The diﬀerences
between the Salt Lake and Reno density proﬁles measured on the same day were foundto contribute an uncertainty to the molecular atmospheric transmission over 40 km of lessthan 3 % over a one year period [93].

3.2.2

The Aerosol Component

The aerosol component is more complicated. Aerosol sizes range from the from the 10−8 m
scale of large molecules to the 10−5 m scale of particulate matter. Their distributionchanges with location. Local dust can be lifted from the desert ﬂoor by the wind andtransported to elevations that are typically less than a kilometer. More distant sources, forexample, forest ﬁres, volcanic erruptions, or manmade pollution can deposit aerosols high3.3. MONITORING THE ATMOSPHERE - LOCAL MEASUREMENTS

65

in the atmosphere to be distributed over tens of km by upper level air ﬂows. The aerosol
distribution also varies with time. For example, a rain or snow storm will remove aerosols
from the atmosphere often leaving near molecular viewing conditions.
The light scattering from aerosols of a speciﬁc size and regular shape can be describedby the Mie scattering theory. In general the scattering probability as a function of angle,
or phase function, is characterized by a forward peak, relatively little scattering at 90◦ andsome enhancement for backwards scattering. The forward peak sharpens as the particle size
increases, as one might expect from diﬀraction theory. Since the molecular phase function
varies much less in this region, an increase in the amount of forward scattered light is a
useful signature that aerosols are present. Of course the precise details of aerosol size, shape,and distribution are not known a priori and one must rely on phenomenologically basedmodels for guidance. A commonly used simulation package called MODTRAN (Moderate
Resolution Transmission) was developed by the US Air Force [94, 95]. It is also distributedcommercially [96]. The package contains aerosol models for diﬀerent regions including a“US Standard Desert” parameterization.

3.3

Monitoring the Atmosphere - Local measurements

Sensitivity to changes in the amount of aerosols is a crucial requirement of any atmosphericmonitoring system. One simple technique used by HiRes for several years is to measurelight scattered out of collimated Xenon ﬂashbulb devices “Flashers” [97]. One of these islocated relatively close to the HiRes1 detector in the geometry shown in Fig. 3.4. This
device ﬁres nearly horizontally 5 times every 7 minutes. HiRes measures its light overa range in scattering angles from approximately 30◦ to 150◦ . The two plots in Fig. 3.5
illustrate the sensitivity to aerosols. As the aerosol content increases, the amount of lightdetected at forward angles (30◦ ) increases. However, the amount of light at large angles(120◦ –150◦ ) remains relatively constant. The ratio of forward scattered light to large angle
scattered light then yields a local measurement of changes in the aerosol content. Using asimple model based on the MODTRAN package [94, 95], this ratio can then be calibrated
to a local horizontal attenuation length.
A one year compilation of ﬂasher data (Fig. 3.6) reveals some interesting features. The
distribution is not symmetric. The sharp edge on one side corresponds to the best caseaerosol-free atmosphere that bounds the atmospheric monitoring problem. The mean valueof the distribution corresponds to an aerosol ground level horizontal scattering length of 20–
25 km. This is longer than the 12 km value for the standard desert parameterization under
the MODTRAN simulation package. A conclusion of this analysis is that at least locally,
the atmosphere at HiRes is clearer than the “standard desert” model. The atmosphere isbetter than “standard desert” and stable on about 70 % of the nights that HiRes operates.
This data as well as similar data accumulated over two years of HiRes prototype operationin 1994–1995 shows that while local measurements are valuable it is still necessary to showthat the atmosphere is homogeneous when it is stable and clear.

CHAPTER 3. ATMOSPHERIC MONITORING

66

111
000
000
111
000
111
000
111

10.6 deg.
60

2935 mFlasher0 m 1668 m

9936 mHiRes 1

HiRes 2

E

12168 m

30

00

S
m

FIG. 3.4: Top view of the geometry of the HiRes intersite Flasher. The ﬂasher elevation
direction 4◦ above horizontal.

(a)

(b)

FIG. 3.5: Hour by Hour measurements of the Intersite Flasher on clear (a) and hazy(b) night. Each of the proﬁles shown covers a scattering angle from 30◦ to 150◦ . The
height of the peak on the left axis is sensitive to changes in the local aerosol concentration.
The forward scattering peak (left side of distribution) in the right ﬁgure has increased incomparison to the left ﬁgure.

3.4. ATMOSPHERIC MONITORING - LONGER RANGE

67

FIG. 3.6: The ratio of small angle scattering to sidewise scattering for the Intersite Flasher
for 1998. The distribution cuts oﬀ on the left at molecular conditions. A “US Standard
Desert” aerosol model has an aerosol attenuation length of 12 km and corresponds to 3.4
on this scale. At 2.6, the average of the data (20–25 km extinction length) indicates theaverage local atmosphere at HiRes is clearer.

3.4

Atmospheric Monitoring - longer range

Lasers are necessary to probe the large aperture in which the TA detectors will observe air
showers. They also provide a signal with important similarities to the signal from an air
shower. The 355 nm light from a frequency tripled Nd:YAG laser is well matched to the357 nm air ﬂuorescence line. The 10 ns pulse width is on the same scale as the thicknessof the charged particle shower front that produces the scintillation light.
Such a laser system [98] (Fig. 3.7) is in use at HiRes. It has been observed by both the
USTA telescopes at Cedar mt. and continues to be observed by the HiRes1 detector. The
beam can be steered in any direction. The laser is specially designed for use in the ﬁeld.
Its polarization and energy can be varied under computer control. The relative energy ofeach shot is measured by a radiometer to an accuracy of about 1 %. The absolute energy
is known to 10 %. A cover protects the steering mechanism from weather when not in use.
A PC running linux controls the system and every component of the system is operated
remotely.
Each hour this system produces a pattern of 1500 shots that are measured by the HiRes1
detector located 12.6 km away. The pattern, shown in Fig. 3.8, includes shots that sweep
through the aperture. Light that has travel a total path length of more than 60 km fromthe laser to the scattering point and then to the detector can be observed on a clear night.
For a given measured signal at the detector, this distance becomes smaller on the hazynight. A second system is being built at HiRes1 to be observed by the HiRes2 detector.
A variety of aerosol parameters have been extracted from the laser data. The aerosol

68

CHAPTER 3. ATMOSPHERIC MONITORING

FIG. 3.7: HiRes2 Steerable Laser system.

(a)

(b)

FIG. 3.8: Range of HiRes2 steerable laser as measured by the HiRes1 detector: (a) Topview; (b) Side-view. The detector that made these measurements is located at 0,0 on theplot. These measurements were made on a night of typical viewing conditions.

3.4. ATMOSPHERIC MONITORING - LONGER RANGE

69

transmission proﬁle as a function of height can be obtained from a collection of laser tracks
where the height and scattering angle is restricted to the region where aerosol scattering ismuch smaller than molecular scattering. (In this analysis, portions of the laser tracks forwhich the scattering angle ranges from 115◦ to 150◦ are selected. These angles should haveminimal aerosol scattering on clear night. Thus the transmission as a function of height isobtained. We have assumed that the aerosols are uniform horizontally. )FIG. 3.9: Aerosol proﬁle from simulated data for a “US Standard Desert Atmosphere.
Circular points show the input parameterization. The vertical scale shows the transmission
vs height for 10◦ viewing angle (4.5 km in height = 25 km horizontal distance).
Figure 3.9 shows results of this calculation for simulated data sample where the aerosol
distribution is known. The data points extend to a height of 4.5 km. The transmission
is calculated for a detector viewing angle of 10◦ which is typical of HiRes and TA. For
reference, 4.5 km at 10◦ corresponds to a point 24 km distant. For this simulated data
sample, the resulting transmission is about 10 % higher than the input value. It should
be noted that an over estimate in the transmission corresponds to an under estimate inshower energy by a similar amount. Distributions for real data, shown for a relatively clear
night (Fig. 3.10 (a)) of typical viewing conditions, and a very hazy night (Fig. 3.10 (b)).
For reference, curves for a “standard desert” aerosol distribution are superimposed on thedata distributions.
As the Japan/US R&D work continues and the second HiRes steerable laser systemcomes on line, it will be possible to test additional analysis techniques. Of particularinterest are those for which the aerosol scattering is small or constant and measurements
at diﬀerent path lengths can be used to obtain the aerosol attenuation lengths. Several ofthese geometries are shown in Fig. 3.11 and Fig. 3.12.
Measurements of the aerosol horizontal attenuation length have also been obtained byscanning near horizontal laser shots with the USTA telescopes that were located 20 km
distant at Cedar Mt. Since the both the laser and the telescopes could be pointed inany direction, the beam could be scanned over an attenuation length at nearly constantelevation. One of these measurements shown in Fig. 3.13 yields a total attenuation lengthof 11 km.

CHAPTER 3. ATMOSPHERIC MONITORING

70
(a)

(b)

FIG. 3.10: Aerosol proﬁle for real data on relatively clear (a) and hazy (b) night.
Rayleigh dominant
at 5-10km altitude
σR (θ2)σR (θ1)
θ2

θ1
L1

5-10km
L2
S1
S2

~30km

FIG. 3.11: Example of a detector laser geometry that can be used to obtain atmosphericattenuation lengths. The telescope observes the scattered light from the a height that is
above the aerosols. The light scattered out of the beam can be described by the Rayleighscattering theory. The attenuation length can be derived from the observation of the lightintensities as a function of path length in the atmosphere.
Beams run on the horizontal planeθscattering
σR+M (θ)

RecieverθσR+M (θ)λ2
θλ2

λ1 extinction for Laser beam

σR+M (θ)λ2 extinction for scattered light

Laser

θ
θ
λ1
σR+M (θ)λ1

σR+M (θ)

FIG. 3.12: Example of a detector geometry for determining horizontal attenuation lengths.
The laser light is observed at a constant height and scattering angle.

3.4. ATMOSPHERIC MONITORING - LONGER RANGE

71

FIG. 3.13: The attenuation of a horizontal laser beam from the hr2sls system as measured
by the USTA telescope at Cedar Mt. The attenuation length by the Mie scattering isestimated to be 28 km.
As part of the R&D eﬀort an initial test of a LIDAR (Light Detection and Ranging)system was conducted at the HiRes1 site [99]. It consisted of a Nd:YAG(355nm) laser
and a nearby 1.5 meter ﬁxed direction mirror that collected the back scattered light andfocused it on to a PMT. The PMT signal as a function of time was recorded by a digital
oscilloscope. Figure 3.14 shows an example measurement made in Utah. The received
light is described by the straight line. Under the assumption of atmospheric uniformity, we
can obtain the transmittance as a function of thickness of atmosphere X. The attenuation
length λ(X) of 1440 g/cm2 is obtained in this measurement.
The LIDAR technique is expected to be very valuable in determining inhomogeneities in
the atmosphere. R&D is in progress to compare LIDAR and side scattered light sensitivity
to aerosol parameters of interest.
distance
6

8

10

12

14

km

20

ln(Pr*R*R/dens(h))

Utah (1600masl)
1998.11.27
laser = 20mJ, <80shots>

19

elevation a. = 3 deg
receptor = 150cm dia
PMT viewing s.a. = 1.85 deg
weather = very fine

18

17
1500

2000

X(g/cm^2)

2500

3000
depth

FIG. 3.14: A measurement made in Utah during a test of a back scatter LIDAR system.
The attenuation length, λ was found to be 1440 g/cm2 for X = 1200 to 3000 g/cm2 during
this test.

72

3.5

CHAPTER 3. ATMOSPHERIC MONITORING

Cloud monitor by Infra-red imaging detector

With infra-red imaging detector, we can sense the temperature of each sky patch. If thecloud appear inside the ﬁeld of view, it show the higher temperature than blue sky region.
With the infra-red imaging detector sensitive to ∼ 10μm photon, we can build high sensitive
cloud monitor system. Mounting these system on the alt-azimuth mount (May be mounted
on the Alt-Azimuth telescope), we can scan the whole sky and make the complete cloudmap, for example, every 10min as shown in Fig. 3.15.
The cloud measurement will play a diﬀerent role from atmospheric clarity measurement.
Existing cloud in the target volume should be treated as dead volume in Telescope Arrayexperiment. When we derive the energy spectrum, this eﬀect should take into account in
the exposure calculation.

FIG. 3.15: The sky picture with 10μ photon. The ﬁeld of view is elevation angle of0◦ − 19.5◦ , and azimuthal angle of 26◦ centered at south direction. The pictures were taken
every 30 seconds. We can see well the movement of cloud.

3.6. ATMOSPHERIC MONITORING SYSTEM FOR TELESCOPE ARRAY

3.6

73

Atmospheric Monitoring System for Telescope Array

The atmospheric monitoring system for the Telescope array will rely on steerable laser
systems to probe the detector aperture. Of course, the TA ﬂuorescence detectors canbe used as optical receivers for atmospheric monitoring. When we use them, there is anadvantage that tens to thousands of PMT’s measure every laser and ﬂasher shot ﬁred
through the detector aperture. We also plan to install the steerable telescopes of 3mdiameter in each station, which have an advantage that the same camera is used to scan
the laser beam for the side scatter measurement and reduce the systematic errors in thephase function measurement. This steerable telescope will also act as a LIDAR receiverfor back scattered light to probe deep in the atmosphere.

FIG. 3.16: LIDAR scanner developed by DFM engineering Inc. in US. The pointing
resolution is 1/100 degrees, and the maximum rotating velocity is 60 degrees/sec. Theinterface with LINUX system is available. This system can be put at the top of the thickpipe located at the center of TA shelter.
In Fig. 3.16, the example of LIDAR scanner is shown. It was developed by DFM engineering, Inc. in US and used by researchers in meteorology. This system will be located at
the top of the thick pipe at the center of the TA shelter. The linux interface is supported inthis system and useful for the remote operation. The pointing resolution is 1/100 degree,
and the maximum rotating velocity is 60 degree/sec. It is water proof. This system maysatisfy our requirements. The laser system and optical system, similar with the HiRes2
laser system, which control the beam intensity and polarization will be installed inside theTA shelter and kept in the constant temperature environment.
The 3 m diameter alt-azimuth telescopes is shown in Fig. 3.17, which is developed as a
Telescope Array prototype detector in Japan. It has pointing resolution of 1/1000 degree
and the maximum rotating speed of 5 degree/sec.
The combination of the high accuracy pointing LIDAR scanner and the high accuracy
alt-azimuth telescope in each station is very powerful. We can shoot laser at any direction
and receive the scatter light from any point in the atmosphere and we can scan all sky
region in both back scatter and side scatter measurement. Side scatter measurement canbe done as an inter-site operation between neighboring two stations. The large diameterof the receiver will allow us the back scatter measurement in wide distance. The LIDAR

74

CHAPTER 3. ATMOSPHERIC MONITORING

FIG. 3.17: Optical receiver for atmospheric monitoring in Telescope Array experiment.
The mirror of 3m diameter is mounted on the alt-azimuth. The pointing resolution is
1/1000 degree and the maximum rotating speed is 5 degree/sec.
measurement at the zenith direction is also possible. There are a lot of freedoms in theatmospheric measurement with these apparatus.
The TA experiment will observe a large amount of atmosphere, roughly 300km by 100km,
or about ten times that of HiRes. Despite the much larger area, details of the atmosphericmonitoring challenge for HiRes and TA have important similarities. TA will be locatedin the same Great Basin desert area of Utah where HiRes is located. Although the 30–40
km intersite distances exceed the 12.6 km separation between the two HiRes stations, thehighest energy showers observed by HiRes are generally 10–30 km away. This distanceoverlaps expected 20–40 km detector/shower separation for TA. The techniques used tomonitor the atmosphere at HiRes will also work for Telescope Array, and the atmosphericmonitor system for Telescope Array can be examined in the HiRes experiment.

Chapter 4
Physics Simulation and Expected
Results
4.1

The TA Detector Simulation

The TA Detector Simulation Package has been developed and maintained for the R&D
works. It consists of three subsets: the Event Generator, the Signal and Background Pulse
Simulator, and the Event Reconstructor. In this section how the ﬁrst two subsets work to
generate simulation data is described brieﬂy.

FIG. 4.1: An example of the simulated event tracks recorded in two stations.

4.1.1

The TA event generator

The Event Generator calculates signal strength produced by atmospheric ﬂuorescence lightemission from an Extensive Air Shower (EAS) with a given geometry, and builds simulation events by calculation of number of photoelectrons in every channels of a PMT camera
in each mirror. It involves the longitudinal proﬁle of an EAS, the models of the atmosphere, the air ﬂuorescence yield, and the detector optics. Simulation of actual pulses withsuperposing the night sky background is performed in the second subset, the Signal andBackground Pulse Generator, which will be described later.
The atmospheric density proﬁle to calculate the physical height hv as a function of
atmospheric vertical depth Xv is given by⎧2⎪⎨ 47.05 − 6.9 ln Xv + 0.299 ln 0.1Xv

hv (km) =⎪⎩48.5 − 6.34 ln Xv
44.34 − 11.861(Xv )2

75

Xv ≤ 25g/cm2
25 ≤ Xv ≤ 230g/cm2
Xv ≥ 230g/cm2

.

(4.1)

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

76

Every dX = 1 g/cm2 along a shower axis, it calculates number of electrons containedin the cascade if the primary cosmic ray has already initiated an EAS, otherwise will
judge whether the primary particle interacts or not with the exponential probability 1 −exp [−dX/λint ] ∼ dX/λint . The number of electrons (the electron size) is calculated by themodiﬁed Gaisser-Hillas function:
Ne (E, X − X1 ) = S0

E

Xmax
exp
−1
λgh



X − X1
Xmax − λgh Xmax −1
λgh

exp −

X − X1
,
λgh

(4.2)



E
S0 = 0.045 1 + 0.0217 ln (
,
(4.3)
)
100TeV
where  74 MeV is the critical energy, X1 is the ﬁrst interaction length, λgh  70 g/cm2
is the attenuation length of the shower proﬁle, and Xmax is the averaged position of shower
maximum in the atmosphere as a function of primary energy E. We use the value of Xmax
by ﬁtting the shower proﬁle from the Corsika Monte Carlo simulation code given byE
Xmax = 58 × log
− 297
1eV

g/cm2

.

(4.4)

In this formula the actual position of shower maximum in an event is given by Xmax +X1 − λint . Consequently X1 sampled for each event causes main ﬂuctuations of the shower
proﬁle event by event. Note that this parameterization gives the radiation length Xrad forhadron-induced showers analytically by




−1
Xrad = S0 λgh exp Xλmax
gh




2π





Xmax
−1
λgh
2



− Xmax −1

Xmax
−1
λgh

λgh

Γ(Xmax /λgh )
.

S0λgh

(4.5)

∼ 32 g/cm

The Generator also has another option to use numerical functions ﬁtted by the shower
proﬁle simulated by the Corsika and/or AIRES Monte Carlo package instead of using theGaisser-Hillas formula given by Eq. (4.2). In this option X1 and Xmax are given directlyfrom the external Monte Carlo shower simulation package.
Number of photoelectrons received by a mirror in each station, which is originated in
atmospheric ﬂuorescence emission from the EAS, is then calculated as follows.
Ne f l (hv )dNpe=
Tsurf TM Amir
dL
4πr2



ΔXdet
dλ exp −
λR



400nm
λ

4

ff l (λ)Q(λ) BG3 (λ)Rmir (λ).

(4.6)
Here f l (hv ) is yield of atmospheric ﬂuorescence, Tsurf is the transmission factor of thesurface reﬂection, TM is the transmission factor of propagation of light taking account of theMie scattering, Amir is area of a mirror, ΔXdet is the atmospheric slant depth between thelocation of a mirror and the light-emission point along the shower axis, ff l (λ) is atmospheric
ﬂuorescence spectrum as a function of wavelength λ, Q(λ) is quantum eﬃciency of a PMT
tube, BG3(λ) is the transmission factor of an optical ﬁlter installed in front of the camera,
and Rmir (λ) is reﬂectivity of a mirror.

4.1. THE TA DETECTOR SIMULATION77

As expressed in Eq. (4.6), the Mie scattering cross section is approximated to be independent of the wave length λ in the current Generator. The transmission factor TM is thenwritten byHM
ln TM = e−h/HM − e−hdet /HM,(4.7)
LM cos θ
where HM is the scale height and LM is the mean free path.
The Cherenkov light emission also makes signiﬁcant contribution to the overall lightintensity especially if an EAS goes toward direction of a station. Because the Cherenkov
radiation is anisotropic, one must consider the distribution of scattered angles during the
propagation of light. Currently the Generator approximates that the angular distribution isdetermined dominantly by its direct Cherenkov emission angle and the Rayleigh scattering
angle whose distribution follows (1 + cos θ2). Thus the overall Cherenkov intensity is
calculated as follows.
ch
dNpe
dL =

Ne f l (hv )Ich (hv )TsurfTM Amir


−θ/θ0
1
det 400nm 4×[ 2πre 2 sin θθ0 dλ exp − ΔX()λRλλ2 Q(λ)BG3 (λ)R mir (λ)θ2 ) dλ(1.0 − exp+ 3(1+cos
16πr 2

400nm 4− dX
λR ( λ ) ) exp



det 400nm 4− ΔX
λR ( λ )

,1
λ2 Q(λ)BG3(λ)R mir (λ)](4.8)
where θ0 is the direct Cherenkov angular scale, dX = 1g/cm is the sampling step in the
program, and Ich(hv ) is intensity of the Cherenkov emission as a function of the height in
the air.
Then an individual photoelectron is given its source photon-emission point in the showercascade taking account of the lateral distribution of air showers following the NKG function.
The vector from the emission point to the detector station is put into the telescope raytracing program to calculate its trajectory to determine a mirror and a tube that receives
the photon.
Repeating the above processes builds an array of number of photoelectrons as a functionof time for every channels. It is passed to the Signal and Background Pulse Simulator.
2

4.1.2

Signal and background pulse simulator

This program simulates pulses in the electronics generated by the photoelectron distribution
calculated by the Event Generator. It also estimates the night sky background intensity
and simulates its contribution.

Charge[pe/200 nsec]

t1

t2

50

0
0

10000

20000

30000

time [nsec]

FIG. 4.2: An Example of the pulse proﬁle simulated by the Pulse Simulator.

78

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

The signal ﬁnding algorithm described in Chapter 2 is then performed for all the recorded
channels to determine the timing window [t1, t2 ] to give the best signal to noise ratio. The
pulse proﬁle within the window is used for the event reconstruction. Figure 4.2 shows anexample of the simulated pulse proﬁle.
Figure 4.3 shows the longitudinal shower proﬁle simulated by the procedure described
here. The angular width of shower track makes diﬀerences of the number of photoelectrons
in diﬀerent tubes viewing the same atmospheric slant depth along the track. The deadspace between the tubes (∼ 2 mm) has also been taken into account in the generator tocause some ups and downs of the proﬁle as seen in the ﬁgure.

Log Recorded photoelectrons

43
Rp[3]37.950 km
2 telescopes triggerd

2

1
500

1000

1500

Atmospheric Slant Depth [g]FIG. 4.3: An Example of the longitudinal shower proﬁle simulated by the TA Monte Carlo.
Each cross shows the number of photoelectrons and the FOV in unit of atmospheric depth of
an individual tube. The vertical line corresponds to the shower maximum of this particular
event.

4.2

The Event Reconstruction

4.2.1

The center-of-gravity constraint

For most of triggered events, the air ﬂuorescence detectors that aim at observing air showers
passing ∼ 30 km away have track lengths which are usually shorter than 15◦ on the PMT
clusters because of the geometrical factor and the attenuation of signals in the atmosphericpropagation. Short track events have several diﬃculties to be reconstructed with great
accuracy. First, the χ2 ﬁtting procedures suﬀer multiple local minima to give the wrong
geometry ﬁtting. Secondly, even when the shower-detector plane can be ﬁtted nicely withthe event track, the true geometry cannot be always resolved because the longer the impact
parameter becomes, the lesser the true geometry depends on direction of the ﬁtted shower
detector plane in each station. Finally the longitudinal shower development gives very
rapid change in the ﬂux along the track, which leads to strong correlation between thegeometrical ﬁtting and shower proﬁle ﬁtting. One needs to know how the ﬂux changes
along the track before the geometrical ﬁtting in order to get better angular resolution.

4.2. THE EVENT RECONSTRUCTION

79

Station 1

r1
is
er ax
Show

r2

Station 2

FIG. 4.4: Concept of the center of gravity constraint. The shower axis can be deﬁned in
two dimensional phase space, r1 and r2 .
The local χ2 problem originates in dealing with too many dimensions of the phase spacein the χ2 ﬁtting procedure. One needs 4 parameters to deﬁne the shower geometry (e.g.,
zenith, azimuth angle, and (x, y) for the core location). Hence we have introduced additional constraint on the ﬁtting to reduce the dimension. Short track events have noredundancy to deal with multiple dimensions.
Direction of the center of gravity of the event track is the one which can be calculated
from the geometrical track information with maximum redundancy. This is determined asfollows:⎛ ⎞
i nxP M T,i × npe,i
1 ⎜ 
⎟
.
(4.9)
ng =
⎝
i nyP M T,i × npe,i ⎠|ng | i nzP M T,i × npe,iHere (nxP M T,i, nyP M T,i , nzP M T,i ) is the unit vector of the central direction of PMT i’s FOV,and npe,i is number of photoelectrons integrated and recorded in channel i.
The direction determined at each station should point the shower track. The Monte
Carlo study actually conﬁrmed that the direction can be determined within ∼ 0.03◦ oﬀ
the track axis. Thus it is very good assumption that the ﬁtted shower axis should crossthe axis of the center of gravity direction (noted as G-direction hereafter). Then only two
parameters of r1 and r2 , lengths along the axis of the G-direction at two stations would
completely deﬁne the shower geometry. Under this constraint, the phase space of thegeometrical ﬁtting is two dimension of r1 and r2 which leads to very robust ﬁtting for mostof the events. This concept is illustrated in Fig. 4.4.

4.2.2

Fast reconstruction for initial guess

The data is ﬁrst processed by the fast reconstruction to give an initial guess of its geometry
before the main reconstruction procedure. The method here is based on the Amplitude
Weighting Method, the simplest and traditional way of using available PMT signal in-

80

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

formation to determine the shower geometry. The shower-detector plane (SDP) at eachstation is determined to minimize the χ2,χ2 = (Δθk )2

σk2

k

wk

,

where
Δθk = cos−1 (npmt,k nSDP ) −σk = 0.3◦ , wk =

npe,k
n̄pe

(4.10)

π2,.

(4.11)(4.12)

Here npmt,k is normal vector of direction viewed by PMT k, n̄pe is averaged number of photoelectrons per channel over an event track, nSDP is the normal vector of the SDP direction.
Then the arrival direction n is determined byn=nSDP,i × nSDP,j|nSDP,i × nSDP,j |.

(4.13)The suﬃx i, j are associated with the stations to trigger the event. When more than
two stations trigger an event, two stations receiving most and second most number ofphotoelectrons are selected to give an initial guess of its arrival direction.
The G-direction deﬁned by Eq. (4.9) and the length of the axis of this direction to theinitially determined shower axis then can be calculated. The determined r1 and r2 set thestarting point for the main ﬁtting procedure described below.

4.2.3

Reconstruction using the pulse proﬁle

The TA front-end electronics based on the ADC-DSPs records the signal proﬁle as a function of the sampling time. Fine geometrical resolution is obtained by minimizing the χ2built by comparison of the prediction of the signal proﬁle by the TA Monte Carlo event
generator with the recorded proﬁle every sampling frequency. This is called the Signal
Wave Form Fitting method.
Sho

wer

Axi

ns

s

ni

tj
in
g

k

ng

Station i

jth

sa

m

pl

li
mp

αj
αj+1

j+1

th

t j+1
ψi

sa

ri

FIG. 4.5: Concept of the Signal Wave Form ﬁtting for the ADC-DSP-based electronics.
tj+1 − tj corresponds to the sampling time (200 nsec for the TA ADC-DSPs).

4.2. THE EVENT RECONSTRUCTION

81

Figure 4.5 illustrates how the event geometry determines the signal proﬁle. The longitudinal direction αj at the station i along the shower track is related to a given event
geometry and relative timing at j-th sampling as follows.


c
ns ri
t
−
t
−
j
0
Rip
c

αj = π − ψi − 2 tan−1

,(4.14)

where Rip is the impact parameter from station i, ns is direction of the shower axis, and ri isthe vector from the station to the core location. The event geometry is deﬁned by the twoparameters r1 , r2 that are the lengths along the axis of the G-direction and t0, the absolute
origin of the timing assuming that the clock at each station is relatively synchronized.
Consequently the signal proﬁle at every sampling time, i.e., how the light spot crosses the
PMT is a function of r1, r2 , and t0 via Eq. (4.14).
In fact the prediction of the signal proﬁle relies on not only the geometrical factor as
expressed by Eq. (4.14) but the other factors: the telescope optics such as spot size andoptical aberrations, PMT response, intrinsic width of the shower track (i.e., lateral distribution of electrons in the cascade), and the longitudinal shower proﬁle. The optics and
PMT response can be simulated by ray-tracing program and the detector Monte Carlo.
The lateral distribution of showers can be reasonably described in the NKG formula asa function of the atmospheric slant depth. Hence this method needs to utilize the full
detector simulation to estimate the expected amplitude in each channel. To deal with thethe longitudinal shower proﬁle, we use the normalization method to average the expected
ﬂux from all PMTs within a certain angular bin along the track based on the assumptionthat the ﬂux change smoothly along the track. In this method the Monte Carlo simulationis responsible for predictions of eﬀects from the optics, the PMT response, and the lateral
distribution of a shower but does not need to consider the longitudinal proﬁle.
Then χ2 to be minimized in the Signal Amplitude Fitting to determine the geometry ofa shower track is given byχ2 =stationM T sampling
 P

i



i,k,j
ni,k,jpe,measured − npe,predicted (r1 , r2 , t0 )ni,k,jpe,measured

j

k

2

,

(4.15)

with the normalization by
Δα

i,k,j

Δα

i,k,j

k

k

npe,predicted |tj =npe,measured |tj.

(4.16)

Here tj is timing at j-th sampling. The angular bin of the normalization in Eq. (4.16), 3◦of Δα, gives the best performance. Several investigations have shown that minimizing theχ2 value only with the channels having better than 4σ of integrated signal-to-noise ratio
over the time window leads to the reasonable reconstruction. The reconstruction program
initially requires two stations with recording more than 5 PMTs with ≥ 4σ.
The χ2 written by Eq. (4.15) still has many local minima. In the initial investigation one
ﬁnds that even the ﬁtting under the center of gravity constraint sometimes trap events in a
local minimum to give the bad geometrical resolution if one performs the ﬁtting in too large
size of the phase space. The risk of the minimization process ﬁnding some local minimum

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS82

is not negligible. Several investigations showed that using the Amplitude Weighting χ2
as a guideline to deﬁne the size of the phase space (r1 ,r2) works well to prevent the poor
ﬁtting. In this method, whenever the Amplitude Weighting χ2 given by Eq. (4.10) reaches
a certain threshold value, the routine stops the ﬁtting further and try a new dimension of
the phase space for another trial as if the ﬁtting procedure “bounced” at a wall.

4.2.4

Reconstruction of longitudinal shower development

Reconstruction of the longitudinal development to determine a ﬁrst interaction point, X1 ,and Xmax is based on the Maximum Likelihood Method. The probability of a photoelectron
arrival at a PMT i from longitudinal angle α along the axis of the shower track is given byi
Pi (σspot, α) =

1Δi⎡

 +Δi /2⎤

1
(α − ψ)2 ⎦
⎣−
√
exp
dψ
2
i
i
−Δi /22πσspot
2σspot.

(4.17)i
The spot size σspot
and pixel size Δi are calculated by the ray tracing program.
This equation based on angular space can be transformed to phase space of the physicalatmospheric slant depth:!

i, X − X0i ) =Pi (σspot

"
dXv "

ri
√

⎡

 Δi
2

× −Δ √
2"

1 − (nni ) dhv ""i1i2πσspot⎢ (exp ⎣−

1
Δi
X=X i
0

⎤

1−(nni ) dhv(X − X0i ) − ψ)2 ⎥
ri
dXv
⎦ dψ
2
i
2σspot

,(4.18)

where ni is normal vector of the FOV direction of PMT i, X0i is the atmospheric slant
depth along the track at center of the FOV of PMT i, ri is a distance from the mirror to
the shower track at the center of FOV, hv is the vertical height of atmosphere and Xv isthe vertical atmospheric depth.
Then we can form a likelihood function for the longitudinal proﬁle of signals along the
track by folding the probability function of Eq. (4.18) with a longitudinal development ofphotoelectrons expected from the air shower:
all




dNe
,
dNpe dXi(4.19)
where κ is the normalization factor, Npe is number of photoelectrons, Ne is electron size as
a function of atmospheric depth given by the Gaisser-Hillas Formula:ln Ll =

nmeasured
× ln
pe,i

κ

i
dXPi (σspot, X − X0i )Ne (X, Xmax , X1 , Nmax )

Ne (X, Xmax , X1 , Nmax) = Nmax

X − X1
Xmax − X1

 Xmaxλ −X1%

Xmax − X
exp
λ

&

.

(4.20)

And dNe /dNpe dX is determined by geometry of track, ﬂuorescence yield, transmission
factors due to the atmospheric extinction, and detection eﬃciency of the detectors, all ofwhich is calculated by the Monte Carlo simulation. Let us remark here that
Ppe (X, Xmax , X1 ) = Ne (X, Xmax , X1 , Nmax )dNe
dNpe dX(4.21)

4.3. APERTURE

83

is the photoelectron distribution expected from the longitudinal development proﬁle determined by Xmax , X1 , and Nmax .
Xmax and X1 are determined by maximizing Ll , and Nmax in Eq. (4.20) is estimated bysummation of detected photoelectrons. The primary energy of the event is given by


E=

Xrad

Ne (X, Xmax , X1 , Nmax )dX,

where Xrad = 34.5 g/cm2 is the radiation length in the atmosphere andcritical energy.

4.3(4.22)
 74 MeV is a

Aperture

In this section the event reconstruction aperture expected in the Telescope Array is described. The TA detector simulation described in the previous sections has generated
simulation data sets for this study. The events are reconstructed when at least 6 PMTs of
one or two neighboring telescopes are ﬁred 4 σ above the night sky background. The total
number of detected photoelectrons and the length of the reconstructed track are shown in
Fig. 4.6 for 1020 eV protons having at least one reconstructed track.
In order to deﬁne the stereo aperture of TA, we required that at least two stations havea well reconstructed track, both of which extend more than 5◦ in the ﬁeld of view (FOV).
Some representative properties of the reconstructed tracks are shown in Fig. 4.7 for 1020 eV
protons. The aperture obtained with this condition is plotted in Fig. 4.8 for 1018 – 1021 eVprotons. It is ∼ 50,000 km2 sr for 1020 eV protons. The location of the shower luminous
center is plotted in Fig. 4.9 for 1019 and 1020 eV protons. The ﬁgure indicates that theshower as far as ∼ 60 km away from the closest station can be detected and reconstructed
for 1020 eV protons. The acceptance for the 1019 eV proton is not concentrated in thevicinity of each station but rather uniformly distributed near the center of the TA site.
The expected event rates are listed in Table 4.1. The events with energies beyond 1020 eV
are detected at 50 events/year assuming the ﬂux of super GZK events measured by AGASA.

Table 4.1: The Cosmic ray hadron annual event rate detected and reconstructed by theTelescope Array. The cosmic ray ﬂux measured by AGASA is assumed.
3 × 1018 eV1019 eV3 × 1019 eV1020 eV

Energy
≤E≤
≤E≤
≤E≤
≤E

Event rate [yr−1]
1019 eV9550
19
3 × 10 eV
1700
1020 eV320
50

Number of events

Number of events

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

84

30
(a)

20

(b)

80

60

40
10
20

0

0

5000

10000

15000

0

20000

0

20

40

60

80

(c)
100

75

100

[degree]Number of events

Number of events

number of pe

150
(d)

100

50
50
25

0

0

2000

4000

6000

8000

0

10000

0

10

20

30

40

(e)
400

200

0

50

[degree]Number of events

Number of events

number of pe
600

(f)

400

200

0

1

2

3

4

5

6

7

8

9

10

Number of stations

0

0

1

2

3

4

5

6

7

8

9

10

Number of stations

FIG. 4.6: (a,b) The number of photoelectrons and the track length for the the station
observing the longest track. (c,d) The same for the station observing the second longest
track of the event. The number of stations with the track length longer than 5◦ (e) and
15◦ .

85

40

Number of events

Number of events

4.3. APERTURE

(a)
30

(b)
20

20
10
10

0

0

20

40

60

80

0

100

0

100

200

(c)

40

20

0

300

[degree]Number of events

Number of events[degree]

60
(d)

40

20

0

20

40

60

80

0

100

0

20

40

60

80

100

[km]

Number of events

Number of events

[km]

60
(e)

40

(f)
30

20

20
10

0
600

800

1000

1200

[g/cm2]

0
-250

0

250

500

750

1000

[g/cm2]

FIG. 4.7: (a) Zenith and (b) azimuthal angle distribution of reconstructed tracks. (c) The
distance from the luminous center of the shower to the nearest station and (d) to the second
nearest station. (e) XM AX and (f) XEN D − XM AX distribution where XEN D means thelast observed point (tail) of the shower. The negative XEN D − XM AX means the shower
maximum was not observed in the FOV.

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

86

Gaiser-Hillas
1000*km*km*str

Corsika

50

0
17

18

19

20

21

22

log(Energy in eV)
FIG. 4.8: The stereo aperture of TA.

North-South [km]1019 eV

10 20eV

100

100

0

0

-100

-100

-100

0

East-West [km]

100

-100

0

100

East-West [km]FIG. 4.9: The projection of shower luminous centers to the ground. The shaded circles
correspond to locations of the 10 stations.

4.4. RESOLUTIONS OF ENERGY, ANGLE AND XM AX

4.4

87

Resolutions of Energy, Angle and Xmax

For the air ﬂuorescence method, there are 3 major factors to inﬂuence the resolution of
measurement.
– Event reconstruction– Atmospheric correction– Pixel calibration (optics and electronics)
The accuracy of event reconstruction is important for all the observables such as the energy,
the arrival direction and the shower maximum Xmax . The atmospheric correction and the
pixel calibration are most relevant for the resolution of energy measurement. Besides theresolution, we need to estimate the accuracy of the measurement in absolute scale, whichis particularly important for the energy measurement.

4.4.1

Accuracy of arrival direction and Xmax

The accuracy of event reconstruction is estimated by comparing the value obtained by theevent reconstruction with the value used for the event generation. The original Xmax usedgen
, is determined by ﬁtting the generated shower proﬁle with Gaisserfor the generation, Xmax
1
Hillas function . The reconstruction resolution of Xmax and the arrival direction is plottedin Fig. 4.10 for 1020 eV protons generated by the CORSIKA simulation code. All the events
satisfying the stereo condition are used except that a few events with large χ2 in the ﬁtting
are excluded. The large χ2 events mostly correspond to the sizable contributions from theCherenkov emission. These events amount less than 3% of the total sample and they canbe recovered by reﬁning the event reconstruction algorithm in future. It is remarkable that
the Xmax and angular resolution distribution have a well controlled shape without a longtail.
In order to determine the reconstruction resolution, we ﬁtted the distribution of Xmax
by the Gaussian. The angular resolution is determined from the integral distribution(Fig. 4.10(c)) as the point below which 68% of the events are contained. The resolution
obtained this way is plotted in Fig. 4.11. It includes the eﬀect of shower ﬂuctuation, thephotoelectron statistics and the systematics originated from the ﬁtting procedure. In tne
same ﬁgure, the resolutions obtained for 1018 –1021 eV protons are plotted.

4.4.2

Determination of energy

As described in §4.2, the energy determination is based on the calorimetric energy integral,which leads to less sensitivity on unknown assumptions concerning the hadron interactions
at extremely high energies. Here let us describe the reliability and systematic uncertainty
on our energy determination with the Telescope Array.
1

We use superscripts gen and rec for the value used for the generation and the value obtained by thereconstruction.

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

Number of events

88

(a)
80

60

40

20

Number of events

0
-200

-100

0

100

200

[g/cm2]

(b)

80

60

40

20

0

0

1

2

3

4

5

Cumulative counts of events[degree]

(c)

1000

1σ

(839, 0.82)

500

0

0

1

2

3

Angle[degree]recgenFIG. 4.10: (a) The Xmax resolution; Xmax
− Xmax, (b) The distribution of the opening
angle between the generated and reconstructed vectors of the arrival direction, (c) Integral
form of (b) obtained for 1020 eV protons generated by CORSIKA.

4.4. RESOLUTIONS OF ENERGY, ANGLE AND XM AX

89

2

Gaiser-Hillas

(a)

30

(b)

[degree]g/cm 2

Corsika

20

1.5

1

10

0.5

Corsika
Gaiser-Hillas
0
17

18

19

20

21

0

22

17

log(Energy in eV)

18

19

20

21

22

log(Energy in eV)

FIG. 4.11: The energy dependence of (a) Xmax resolution and (b) angular resolution.
Energy of the EAS is determined by Eqs. (4.6) and (4.22):
E=

dep

Tsurf AmirdL 4πr2
dXNpe (X)dX f l TM%&−1dλff l (λ)Tray (λ, X) det (λ),(4.23)

where dep = /Xrad is energy deposit of charged particles in EAS per unit atmosphericdepth, Tsurf is the transmission factor of the surface reﬂection, TM is the transmission
factor of propagation of light taking into account the Mie scattering, Amir is area of themirror, f l is yield of atmospheric ﬂuorescence, ff l (λ) is atmospheric ﬂuorescence spectrum,
Tray is the transmission factor due to the Rayleigh scattering in the light propagation, anddet is the overall detection eﬃciency such as the mirror reﬂectivity, quantum eﬃciency of
the tube, the ineﬃciency due to the dead space and the data recording, and the opticalﬁlter transmission, all of which is measurable and estimated by the detector Monte Carlosimulation with ray-tracing of the detector optics.
What we observe is Npe in Eq. (4.23), the number of photoelectrons per unit slant depth
along the shower axis. The geometrical term 4πr2 , the air ﬂuorescence yield f l , and theRayleigh scattering term Tray are determined from the event geometry. Consequently theaccuracy of estimation on the event geometry would aﬀect the ﬁnal resolution of the energy
determination. These terms, however, change only gradually along the path integral overdX. Thus energy estimation is rather robust without heavily relying on accuracy of thegeometrical term. The energy is then approximately given by
E∼
∼



4πR2
dL dep
dXNpe (X) dX[TM dλff l (λ)Tray (λ, X) det (λ, X)]−1
Tsurf Amirf l
4πR2 dL dep
1
dXNpe (X) dXAmir
f l overall (X).

(4.24)

Here R is the distance from the station to the shower luminous center and the geometrical factors are represented at the location where the shower cascades has its maximum
development. overall is the overall transmission factor taking into account the atmospheric
extinction and the detector related eﬃciency det . This equation shows that our energy determination is based on the slow function of the energy integral term, dXNpe (X)/ overall ,which gives the stable resolution of our energy estimation by the Telescope Array.

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

90

Number of events

15

%
200

Corsika(a)(b)

Gaiser-Hillas
10

150

100
5

50

0
-100

0

-50

0

50

100

17

18

19

20

21

22

log(Energy in eV)[%]

FIG. 4.12: The Energy Resolution distributions;(E rec − E gen )/E gen (a) and the resultant
energy resolution as a function of shower energy (b)Figure 4.12(a) shows the energy resolution distribution obtained for 1020 eV protons
generated by the CORSIKA simulation code. As we expected, it is well represented by theGaussian distribution, which is crucial for a reliable measurement because the cosmic rayenergy spectrum is sharply falling with energy. The resolution is ∼ ±6 % over the wide
energy span from 3 × 1018 to 1021 eV as shown in Fig. 4.12(b).
As one can see in Eq. (4.24), the systematic uncertainties on the energy estimation mainly
arise from the following factors:– Uncertainties on the detector eﬃciencies det , which is calculated by the detector
Monte Carlo in the energy determination procedure.
– Uncertainties on the air ﬂuorescence yieldf l.

– Uncertainties on the charged particle energy deposit

dep .

– Energies carried by neutrinos and muons.
– Uncertainties on the factors concerning the atmospheric extinction, TM and Tray .
The ﬁrst term, the detector eﬃciencies are measurable/predictable by our detector calibration and the detector Monte Carlo simulation. The overall uncertainty is estimated tobe 10 %.
The second term, the ﬂuorescence yield f l has been well measured by a laboratory
experiment [90]. The yield for low energy electrons below 1 MeV is not quite understood,
however, and the uncertainty is given as ∼ 10 %.
The energy deposit per unit atmospheric length dep is based on our knowledges of theparticle interactions. It is known to have slight dependences on the age of EAS cascade andthe primary mass initiating an EAS. The canonical number for electromagnetic cascades
is 2.0 MeV/(g/cm2). The modiﬁed Gaisser Hillas function given by Eq. (4.2) gives 2.31
MeV/(g/cm2). The CORSIKA full Monte Carlo simulation gives 2.19 MeV/(g/cm2) with

4.4. RESOLUTIONS OF ENERGY, ANGLE AND XM AX

91

some dependences on the primary particle mass. The uncertainty have been estimated tobe ∼ 5 % mainly because of the dependences on the shower age and the threshold energyof secondary electrons and photons in the simulation.
Energies carried by penetrating particles like neutrinos and muons must be taken into
account to estimate primary energy of cosmic rays from the air shower energy determinedby Eq. (4.23). The full Monte Carlo simulation can calculate the fraction of these missing
energies. The CORSIKA simulation gives this fraction as

EEprimary= 0.959 − 0.082
18
E
10 eV

−0.15.

(4.25)

for average behavior of protons and irons. Uncertainty of 5 % has been estimated due tolack of knowledge of primary mass.
The last term related on the atmospheric extinction is expected to make major contributions to the overall uncertainty on the energy estimation. We discuss the resultant
systematics in detail next.

4.4.3

Atmospheric correction[%]

The energy resolution may be signiﬁcantly aﬀected by the atmospheric correction. In
Fig. 4.13, we show a scatter plot of the extinction caused by the Mie scattering vs the
distance from the shower luminous center to the station for 1020 eV protons. As shown, theaverage extinction by the Mie scattering reaches 0.7 for showers more than 40 km away,
but it saturates beyond this limit.

100
80
60
40
20
0

0

20

40

60

80

100

[km]
FIG. 4.13: Scatter plot of the distance from the shower luminous center to the station vsMie extinction. It is plotted for the nearest station to the shower center.

92

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

FIG. 4.14: Eﬀect of wrong Mie scattering coeﬃcient. The resolution for energy (DE inunit of %), Xmax (DXMAX in unit of g/cm2 ) and angle (DANG in unit of degree) areplotted. The solid line histogram is reconstructed with correct atmospheric parameters(LM = 20 km and HM =1.2 km.) The broken line histogram used LM = 15 km and dottedline histogram used LM = 35 km when reconstructed. The HM was taken 1.2 km for bothcases.

4.4. RESOLUTIONS OF ENERGY, ANGLE AND XM AX

93

30

Scale Height is fixed at 1200 [m]%Attenuation Length is fixed at 20 [km]

50
20

%

0

0

-20

0

10

20

30

-30

40

500

Attenuation Length [km]g/cm 2g/cm 2

20

1500

2000

2500

Attenuation Length is fixed at 20 [km]Scale Height is fixed at 1200 [m]

40

1000

Scale Height [m]

20

0
0

-20
-20

0

10

20

30

40

Attenuation Length [km]

500

1000

1500

2000

2500

Scale Height [m]FIG. 4.15: (a) The change of reconstructed energy by using various “wrong” values of LM
and the “correct” value of HM in reconstruction. The values used for the event generation
were LM =20 km and HM =1.2 km. The error bar represents the resolution of reconstruction.
(b) The same by using various “wrong” values of HM and the “correct” LM . (c) The changeof reconstructed Xmax with “wrong” LM . (d) The same with “wrong” HM .

94

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

The simulation program uses 20 km for the attenuation length by the Mie scattering(LM in Eq. (4.7)) at the ground level. The density of the scattering center decreases exponentially with the height with the scale height of HM =1.2 km. Both generation andreconstruction use the same values of LM and HM . We studied the eﬀect of the Miescattering uncertainty by intentionally taking a diﬀerent set of parameters for the generation and reconstruction of events. An example showing the diﬀerence of reconstructedenergy, Xmax and arrival direction for such cases is given in Fig. 4.14. It is seen that event
reconstruction with wrong understanding of the atmospheric transparency could lead toboth larger systematic shift and poorer resolutions on the energy determination. On theother hand, the angular reconstruction had no inﬂuence of wrong atmospheric parameters
because our method to determine event trajectories is decoupled from the procedure toreconstruct longitudinal shower proﬁle (see §4.2).
The eﬀect of taking a wrong LM and HM for the reconstruction is summarized in Fig. 4.15.
Although the systematic shift caused by reconstructions with the wrong parameters is
not negligible, it should be remarked that the results suggest that 10% shift of averagereconstructed energy is equivalent to ΔLM = +6
−3 km, or ΔHM = ± 0.7 km where ΔLM
and ΔHM are the errors of LM and HM . We believe this level of accuracy can be achievedby the laser calibration. The extinction by the Rayleigh scattering can be calculated
reliably and its contribution to the systematic uncertainty is negligible compared with theMie scattering. We estimate that the energy uncertainty arising from the atmosphericcorrection can be controlled at the level of 10%. The Xmax was aﬀected by the wrong
atmospheric parameters by average shift of ±5 g/cm2 .

4.4.4

Uncertainty of measurement

The measurement of EHE cosmic showers has no convenient way of calibrating the energy
scale. However, the accuracy of the measurement can be estimated directly from theuncertainties of the numbers used for the energy calculation. The accuracies we intend toachieve in TA for these numbers are listed in Table 4.2. The major contributions are fromthe uncertainties of scintillation eﬃciency, calibration, atmospheric correction and overall
shower correction each at the level of 5∼10%. A quadratic sum of all factors in the tablegives 20% and this is the accuracy of absolute energy we expect to achieve at TA.
The uncertainty of angle determination is dominated by the reconstruction error alreadytaken into account in the simulation. The absolute alignment of PMT and telescope canbe calibrated with an accuracy better than 0.1◦ by shooting the laser from the center ofthe station.
The simulation indicates that the value of Xmax changes depending on which functional
shape to be used for ﬁtting the longitudinal proﬁle near the shower maximum. This difference is approximately 15 g/cm2 . The discrepancy between the generated and the reconstructed Xmax is comparable to this shift as illustrated in Fig. 4.10. We take 15 g/cm2 as
the systematic uncertainty of measuring the Xmax . It should be noted that the diﬀerent
shower simulation programs predict diﬀerent Xmax for the particles with the same energy.
For example, Xmax is 827 g/cm2 for 1020 eV proton by CORSIKA whereas AIRES predicts
863 g/cm2 . The ability of TA to discriminate primary cosmic ray particle mass will besigniﬁcantly improved if the theoretical understanding of cascade shower improves and the4.5. DETECTION OF EHE NEUTRINOS

95

prediction of the Monte Carlo becomes more reliable.
The resolution and systematic uncertainties of energy, angle and Xmax measurement issummarized in Table 4.3 for 1020 eV protons.
Table 4.2: Estimated systematic uncertainties of energy measurement
Item
Number of photoelectrons N pe
Fluorescence yieldflDistance to shower
R
Detection eﬃciency
det

Error
5%
10%
5%
10%

Energy loss rate
Atmospheric correction
Missing energy correction
TOTAL

5%
10%
5% the primary particle mass dependences
20% quadratic sum of alldep

TM , Tray
Eprimary /E

Comments
inc. pressure uncert.
error in R2
5% for mirror, 5% for ﬁlter,
8% for PMT, 3% for obscuration.

Table 4.3: Resolution and systematic accuracy of TA
Observable
Energy
Angle
Xmax

4.5

(unit) Resolution Sys. Uncert.
(%)
6
20
◦
0.8
0.1
( )
(g/cm2 )18
15

Detection of EHE Neutrinos

The expected EHE neutrino ﬂuxes are in the range 1 ∼ 30νs km−2 yr−1 sr−1 above 1019 eV
and their detection requires a detector of huge aperture considering the low neutrino crosssections. The standard type underground neutrino telescopes, which observe long-range
upward-going muons with eﬀective areas of 0.1 km2 or smaller, would not be capable of
EeV neutrino detection [102]. An alternative detection method is to search for extensive air
showers (EAS) initiated by electrons/hadrons produced by neutrinos through the charged
current process νl + N → l + X. Showers developing deep in the atmosphere must be
produced by penetrating particles. The Fly’s Eye experiment searched for such an eventto get an upper bound on the EHE neutrino ﬂux [57, 103]. Similar to the Fly’s Eye,
the Telescope Array measures EHE cosmic ray air showers using air ﬂuorescence but withmuch better resolutions and larger aperture. It can reconstruct the EAS development as afunction of atmospheric depth with better than 30 g/cm2 resolution and easily distinguishnormally developing showers from deeply penetrating showers (DPS).

96

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS
3

1500g

zenith > 65 deg.
Reconstructed

LOG [Events / 20g]

P
2

ν
1

0

-1
0

2000

4000

6000

8000

2

Xmax [g/cm ]FIG. 4.16: Reconstructed Xmax distribution for cosmic ray protons with energies of 1019
eV or greater (shown by the red hatches) and neutrinos. Number of events of the protons
corresponds to one year observation by Telescope Array.
The interaction length of cosmic ray hadrons and gamma rays is 50 ∼ 100 g/cm2 near 1019
eV. Thus the probability of these particles initiating EAS at deeper than 1500 g/cm2 is ∼3×10−7 , so any shower starting that deep in the atmosphere would be a candidate neutrino
event. In fact the miss-reconstructed proton induced showers could constitute a backgroundin the neutrino search because of the tail of distribution of the Xmax reconstruction errors.
It should be remarked, however, that the excellent resolutions of the Telescope Arraygiven by the data criteria as illustrated in §4.5 shows that the discrimination of the proton
induced showers from the DPS would be experimentally robust. Figure 4.16 shows the Xmax
distribution for both proton and neutrino induced showers simulated and reconstructed by
the TA Monte Carlo. One can see that none of the proton events has left over in the regionof Xmax deeper than 1500 g/cm2 . A search for a DPS with Xmax ≥ 1500 g/cm2 indeed
excludes the hadron background.
Detection rates can be obtained by folding the predicted ﬂuxes with the product of thecharged current neutrino-nucleon cross section, σνN (E)  2.82 × 10−32 (E/10 EeV)0.402 cm2[102], and the acceptance A(E). The following equations give the event rate [53]:dN(≥ Eνe ) =
dt

∞







dEνe J (Eνe )Dν (Eνe ),(4.26)

Eνe

where Dν (Eνe ) is the “eﬀective aperture” which is folded with the cross section:
EνeDν (Eνe ) = NA

T (Ee ) =

dEe
0

dσνe
(Eνe )T (Ee )dEedΩ(XΩ − 1500[g/cm2])A(Ω, Ee ),(4.27),(4.28)

4.5. DETECTION OF EHE NEUTRINOS

97

where σνe is the cross section of the charged current process with the nucleon, Ee is theenergy of the produced showers, NA is Avogadro’s number, XΩ is the slant depth of theatmosphere for the solid angle Ω, and A(Ω) is the acceptance of the air ﬂuorescence detector
for deeply penetrating showers. T (Ee ) represents the eﬀective aperture column density(km2 sr g/cm2 ) of the detector for the DPS.

Target Volume[ton sr]

Stereo Reconstruction

1.5e+11

1e+11

5e+10

0
18

18.5

19

19.5

20

20.5

LOG(ENERGY[eV])FIG. 4.17: The eﬀective target volume for the DPS. Thick curve: Results obtained by the
TA Monte Carlo simulation. Thin curve: Results obtained by the analytical formula.
The Monte Carlo detector simulation can calculate the eﬀective target volume T (Ee ).
Figure 4.17 shows the results by the simulation. Target volume is ∼ 107 km2 sr g/cm2 ∼1011 ton sr for 1020 eV showers. The results are consistent with the analytical formula [53]given by
⎡



Nst ⎣
h
) 1.1 × 106
T (Ee )  (
10
8.4km



r0
8km

4
5



f 2 − 7 × 105

h
8.4km

2 ⎤
⎦

[km2 sr g/cm2 ],(4.29)

where


⎡



Ee
n
⎣ th
−
log
f = 3.3 + log
1020 eV4σDν (Eνe ) ∼ 5 × 10



Nst
10



Eνe
1020 eV

eef f
4m−1

−1 



'
(

Rmir −1 (
nN B
)
1.5m
106 m−2 sr−1 μs−1⎤tgate ⎦,
5μs
(4.30)
for accounting the detector related S/N, Nst is the number of the station, nN B is thenight sky photon intensity and tgate is the time window for collecting signal, eef f is theﬂuorescence light yield from an electron (photons per meter), Rmir is the radius of thetelescope mirror, h is the atmospheric scale height (∼ 7.5 km), and r0 is the extinction
length of light due to the atmospheric scattering.
The eﬀective aperture Dν (Eνe ) is approximately given by
−2

r0
8km

0.402 Eνe
3.3 + log
1020 eV2[km2 sr].

(4.31)

98

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS
6

LOG (Aperture [m 2 sr])Stereo Reconstruction

5.5

νe
νμ

5

4.5

4
18.5

19

19.5

20

LOG(ENERGY[eV])FIG. 4.18: The eﬀective aperture for detection of the EHE neutrinos.
The detailed Monte Carlo simulation together with the numerical integral of Eq. (4.27)
has obtained the consistent results as plotted in Fig. 4.18 showing that the Telescope Arrayhas the eﬀective neutrino aperture of ∼ 0.3 km2 sr for energies of 1020 eV. Note that theinelasticity for the neutrino-nucleon interactions makes the diﬀerences between the aperturefor electron-neutrinos and that for muon-neutrinos because high energy muons induced bymuon-neutrinos would not contribute detectable air showers.
The expected neutrino event rate for the Top Down models [38] and the “Z-burst”
scenario [44] that the EHE neutrino beams colliding with the neutrino dark matter are
sources of the highest energy cosmic rays (see §1.4) is summarized in the Tables 4.4 and
4.5.

4.6

Identiﬁcation of EHE γ-rays

Some viable models to explain the EHE cosmic rays have predicted that the major primary
composition at extremely high energies is γ-rays. A photon has no electric charge and would
neither be bended by the galactic nor extragalactic magnetic ﬁeld. Identiﬁcation of thepossible γ-ray population would be thus of great importance to resolve the mystery of theEHE cosmic rays.
It has been suggested that the photon-induced air showers might have diﬀerent longitudinal development proﬁle than hadron induced showers. The LPM eﬀect [104, 105] leads tovery slow shower development with signiﬁcant ﬂuctuations due to the possible mechanismsof suppression of bremsstrahlung and pair creation processes at extremely high energies.
On the other hand, the geomagnetic cascading starting with electron-positron pair creationin the geomagnetic ﬁeld at out of atmosphere [106, 107] also aﬀects shower curve but withmuch faster development than those of LPM showers and the feature is strongly related
to the arrival direction. In this section we report the diﬀerences on longitudinal development initiated by hadronic and γ-ray primaries, and discuss on a possibility of γ-ray
identiﬁcation.

4.6. IDENTIFICATION OF EHE γ-RAYS

99

Table 4.4: The expected event rate [/10yr] for some viable Top Down scenarios explaining
the cosmic rays at least above 100 EeV.
Modes
qq
qq
νν
νν

Fragmentation mX [GeV]SUSY
no-SUSY
-

1016
1016
1013
1014

Event Rate
E ≥ 3 × 1018 eV
1.271(νe ) 1.476(νμ )0.492(νe ) 0.604(νμ )7.511(νe ) 6.195(νμ )1.000(νe ) 1.306(νμ )Event Rate
E ≥ 1019 eV
0.837(νe ) 0.986(νμ )0.379(νe ) 0.466(νμ )6.627(νe ) 5.095(νμ )0.194(νe ) 0.186(νμ )Table 4.5: The expected event rate [/10yr] for the Z-burst scenario [44].
fν∗

Event Rate
Event Rate19
E ≥ 1020 eV
E ≥ 10 eV1000 0.154(νe ) 0.331(νμ ) 0.075(νe ) 0.179(νμ )300 0.459(νe ) 1.005(νμ ) 0.227(νe ) 0.552(νμ )20a 5.302(νe ) 11.722(νμ ) 2.649(νe ) 6.448(νμ )∗the overdensity factor of eV mass neutrino dark matter over a supercluster scale of ∼ 5
Mpc.
athe lower bound allowed by the EGRET diﬀuse γ-ray limit. This case sets an upperbound for EHE neutrino intensity in the Z-burst scenario.

4.6.1

Simulation of hadronic and γ-ray shower

To study on the proﬁle of air shower development initiated by γ-rays and hadrons (proton
or iron) the AIRES [108] simulation code with QGSJET hadronic interaction model has
been used in this work. AIRES code uses EGS4 program code for simulation of electromagnetic showers and the LPM eﬀect is included, but the interaction with magnetic ﬁeld
is not incorporated in itself. We developed our own code for electromagnetic cascadingin the geomagnetic ﬁeld. To simulate showers from EHE γ-ray showers, ﬁrst we modeledcascading in the geomagnetic ﬁeld starting with a single photon far away from the Earth’s
surface down to the top of atmosphere. Then secondary particles that reach at the top of
atmosphere were set as an input for AIRES code. An air shower initiated by a single EHE
γ-ray is constructed as a superposition of lower energy γ-ray subshowers.
Main elementary processes leading to particle multiplication in magnetic ﬁeld are magnetic bremsstrahlung and magnetic pair production. It is well known that the essentiallynon-zero probabilities for magnetic bremsstrahlung and pair production require both strong
ﬁeld and high energies [109]. The relevant parameter determining the criteria for this is:χ=ε H
mc2 Hcr,(4.32)

100

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

where ε is the particle energy, H is the magnetic ﬁeld strength (the component normal tothe particle trajectory), m is the electron mass and Hcr = 4.41 × 1013 G.
The total probabilities (cross sections) for radiation and pair production for a given valueof the magnetic ﬁeld strength depend only on χ. Magnetic pair production has signiﬁcantprobability for χ ≥ 0.1 but for eﬀective shower development one needs even higher valuesof χ (χ ≥ 1) because the radiated photon spectrum becomes harder with increasing χ .
We used the diﬀerential probabilities (per unit length) for magnetic bremsstrahlung andmagnetic pair production [110] given by the expressions:

π (ε, ω) dω =

⎡
⎤

 ∞


⎥
ε
ε−ω
2u
αm2 dω ⎢√ 2 ⎢K2− K 1 (y) dy ⎥
+
⎣
⎦,
3
3
ε
ε
ε−ω
3χ

π 3

2u
3χ

⎡





ε
ω−ε
αm2 dε ⎢√ 2⎢+K2γ (ω, ε) dε =
⎣
3
ε
ω−ε
π 3ω



2u1
3χ



∞

+
2u1
3χ

⎤

(4.33)⎥

K 1 (y) dy ⎥
⎦,
3

2

ω
ω
, u1 = ε(ω−ε).Parameter
where ε and ω are the electron and photon energy and u = ε−ωχ was deﬁned above. Here h̄ = c = 1. Kν (z) =∞0e−zch(t) ch(νt) dt is a modiﬁed Bessel

function known as MacDonald’s function.
While for χ
1 (strong ﬁeld) the electromagnetic cascade develops similarly to thecascade in matter[111], in the region χ ≤ 1 (Earth’s magnetic ﬁeld) the photon interaction
length increases sharply with decreasing photon energy. Electrons continue to radiate andthe shower becomes a bunch of photons carrying ≥ 94 − 95% of the primary energy.
In our simulation we used the International Geomagnetic Reference Field (IGRF) andWorld Magnetic Model (WMM) which provides a good approximation of the Earth’s magnetic ﬁeld up to 600 km from the ground and its extrapolation above this altitude.
We have simulated the electromagnetic cascading by injecting EHE γ-rays at a distanceof 3 Earth’s radii from the surface of the Earth. An γ-ray and secondary particles are propagating via pair production and bremsstrahlung. Interaction probabilities are calculated
each step of of every 10 km. Only particles above threshold energy of 1015 eV were followedin the simulation until they reach at the top of atmosphere (50 km above the ground level).
This threshold energy is enough low to neglect the contribution of sub threshold particles
in the cascade.
Interaction probabilities of incident γ-rays with the geomagnetic ﬁeld has been estimatedfor diﬀerent zenith and azimuthal angles of their arrival directions. Figure 4.19 shows
probability maps for γ-ray conversion for 4 diﬀerent primary energies in coordinates ofzenith and azimuthal angles. The region with a smaller probability is centered at 39◦ ina zenith angle and a direction of 14◦ west from the south. The size of this ”window” isshrinking quickly with an increase of primary energy, and most primary γ-rays with energies
greater than 1020 eV initiate the geomagnetic cascade before the top of atmosphere. Averageenergy spectra of secondary γ-rays and electrons at the top of atmosphere are shown in4.6. IDENTIFICATION OF EHE γ-RAYS
N

N

W

E

50

W

100%

0

S

100%

50

0

S

LogE=20.5

100%

50

Conversion Probability

W

E

W

E

S

Conversion Probability

N

N

E

S

0

101

0

50

100%

Conversion Probability

Conversion Probability

FIG. 4.19: Maps of γ-ray conversion probability for primary energies of 1019.5 eV, 1020.0
eV, 1020.5 eV, and 1021.0 eV. Inner Circles show zenith angles of 30◦ and 60◦ and horizon.
Dashed lines correspond to the angular distances of 30◦ , 60◦ and 90◦ to the inverse directionof geomagnetic ﬁeld at Utah.
21

21
o

LogE
21.0
20.5
20.0
19.8

o

North

LogE
21.0
20.5
20.0
19.8

20

Log(EdN/dLogE[eV])

Log(EdN/dLogE[eV])20

theta=39.7

19

18

17

18

19

19

18

16
16

17

18

19

20

21

16

Log(Particle energy[eV])

17

20

21

Log(Particle energy[eV])

21

21
o

LogE
21.0
20.5
20.0
19.8

theta=54.0

o

North

LogE
21.0
20.5
20.0
19.5

20

Log(EdN/dLogE[eV])20

Log(EdN/dLogE[eV])

South

17

16

19

18

17

theta=54.0

South

18

19

19

18

17

16

16
16

17

18

19

20

21

16

Log(Particle energy[eV])

17

20

21

Log(Particle energy[eV])

21

21
o

LogE
21.0
20.5
20.0
19.5

theta=61.6

o

North

LogE
21.0
20.5
20.0
19.5

20

Log(EdN/dLogE[eV])20

Log(EdN/dLogE[eV])theta=39.7

19

18

17

theta=61.6

South

18

19

19

18

17

16

16
16

17

18

19

20

Log(Particle energy[eV])

21

16

17

20

21

Log(Particle energy[eV])FIG. 4.20: Energy weighted spectra of secondary γ-rays and electrons at the top of atmosphere for primary γ-ray energies of 1019.5 eV (open circles),1020.0 eV (open square), 1020.5
eV (solid circles), and 1021.0 eV (solid square) with 3 diﬀerent zenith angles (39.7◦ , 54.0◦
and 61.6◦ ). Azimuthal angles are assumed as north and south.

102

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

Fig. 4.20. Energy spectra for primary γ-rays with energies of 1019.5 , 1020.0 , 1020.5 and1021.0 eV are drawn in each frame. Zenith angles are sampled in 39.7◦ , 54.0◦ and 61.6◦ andazimuthal angles are assumed as north and south. Shapes of energy spectra change with
diﬀerent arrival directions at a ﬁxed primary energy, and primary γ-rays without interaction
to geomagnetic ﬁeld could be found at the right end of energy spectra in speciﬁc cases,
which makes dominant contributions to the ﬂuctuation of the cascade proﬁle due to the
LPM eﬀect.
Each secondary γ-ray and electron generated by the geomagnetic cascade initiates electromagnetic sub air showers. Air shower simulation has been performed using the AIRES
code with QGSJET hadronic interaction model of thinning level of 10−5 . Next, we present
the feature of the electromagnetic air shower proﬁles after the geomagnetic cascades.

4.6.2

The Longitudinal development of γ-ray induced showers
and its identiﬁcation

Shower characteristics depend on primary energy and arrival direction because the LPM effect and cascading in the geomagnetic ﬁeld are aﬀected by particle energy and geomagnetic
ﬁeld strength.
Examples of individual shower developments initiated by primary γ-rays are shown in
Fig. 4.21. Primary γ-rays with energies of 1019 , 1020 and 1021 eV and zenith angle of 54.0◦
and 61.6◦ are shown in these plots. Shower developments from directions of south and north
are shown in left and right ﬁgures, respectively. Shower developments with E0 = 1020 eVfrom south are largely ﬂuctuated in comparison with ones of other primary energies, asseen in Fig. 4.21. The reason is that the LPM eﬀect contributes strongly to a shower
development of γ-ray which does not interact with the geomagnetic ﬁeld. On the other
hand, developments of showers from north and/or ones with much higher primary energy
show faster proﬁles with smaller ﬂuctuations due to the geomagnetic cascading process.
Figure 4.22 shows average Xmax as a function of primary energy. Average Xmax of γray primary has been calculated with zenith angles of 54.0◦ and 61.6◦ (open circles andcrosses,respectively) and the cases of south/north arrival directions. Ones of proton andiron primaries are also plotted with solid and broken lines in the same ﬁgure. Though average Xmax of proton and iron showers are increasing with a constant rate(elongation rate),
one of γ-ray shower has much larger elongation rate in comparison with hadronic showers
and the rate becomes a larger because of the LPM eﬀect. The geomagnetic cascading starts
its contributions to air shower development above energies of several times 1019 eV which
depends on the arrival direction of γ-ray. Then, average Xmax is decreasing and reaches at
the minimum values.
The Xmax distributions for showers initiated by protons and γ-rays with energy of 1019.5 ,1020 and 1020.5 eV and zenith angle of 39.6◦ , 54.0◦ and 61.6◦ are shown in Fig. 4.23. All
distributions here are shown as ones after taking into account a detector resolution todetermine Xmax of ∼ 30 g/cm2 . Typically, Xmax distribution of γ-ray with energy of 1020
eV and zenith angle of 54.0◦ distributes broadly because LPM showers and showers withgeomagnetic cascading eﬀect are mixed together.

theta=54.0
North

103

Log(Nubmer of charged particles)

Log(Nubmer of charged particles)

4.6. IDENTIFICATION OF EHE γ-RAYS

12

10

8

theta=54.0
South

12

10

8

6

6
0

500

1000

1500

0

2

1000

1500

2

Slant Depth [g/cm ]theta=61.6
North

12

10

8

6

Log(Nubmer of charged particles)

Slant Depth [g/cm ]Log(Nubmer of charged particles)

500

theta=61.6
South

12

10

8

6
0

500

1000

1500
2

Slant Depth [g/cm ]

0

500

1000

1500
2

Slant Depth [g/cm ]FIG. 4.21: Longitudinal developments of individual showers initiated by γ-rays with energies of 1019 eV, 1020 eV, and 1021 eV with various injection directions. Left and rightﬁgures correspond to ones of showers from north and south, respectively. Broken lines show
average developments of proton initiated shower with same energies.

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

104

Xmax [g/cm**2]

AIRES for P & Fe
Geomag. Cas. + AIRES for gamma(sec theta=1.7 & 2.1)

South

1000

North
gamma
800

Proton
Fe

600
17

18

19

20

Log(Primary Energy[eV])FIG. 4.22: Average Xmax for showers initiated by proton, Fe and γ-ray as a function ofprimary energy. Proton and Fe showers were simulated with AIRES-QGSJET. Xmax of
γ-ray showers from south and north with zenith angles of 54.0◦ and 61.6◦ are shown.

4.7. THE OBSERVATIONAL POWER TO DISTINGUISH DIFFERENT MODELS 105
LogE=19.5

LogE=20.0

theta=39.7otheta=39.7

theta=39.7o
200

100

0
500

CountsCounts200

Counts200

LogE=20.5
o

100

100

1000

0
500

1500
2

1000

LogE=19.5

LogE=20.0
theta=54.0

LogE=20.5otheta=54.0o

Counts200

CountsCounts

200

100

1000

0
500

1500
2

100

1000

LogE=19.5

LogE=20.0

theta=61.6otheta=61.6

LogE=20.5otheta=61.6oCountsCountsCounts

200

100

1000

1500
2

1500

Xmax[g/cm ]200

Xmax[g/cm ]1000
2

Xmax[g/cm ]

100

0
500

0
500

1500
2

Xmax[g/cm ]

200

1500

Xmax[g/cm ]theta=54.0o

100

1000
2

Xmax[g/cm ]

200

0
500

0
500

1500
2

Xmax[g/cm ]

0
500

100

1000

1500
2

Xmax[g/cm ]

0
500

1000

1500
2

Xmax[g/cm ]FIG. 4.23: Xmax distributions for proton and gamma-ray showers with energies of 1019.5 eV,1020 eV and 1020.5 eV (left, center and right, respectively). Zenith angles of 39.7◦ , 54.0◦ and61.6◦ (top, center and bottom, respectively) are assumed. Xmax distributions of gammaray showers with arrival directions from south and north are shown in separately. All
distributions here are shown as ones after taking into account a detector resolution for
Xmax of ∼ 30g/cm2 .

4.7

The Observational Power to Distinguish Diﬀerent
ModelsWe have seen the capabilities of the Telescope Array to measure the highest energy cosmic
rays. Now the question is how we will be able to distinguish the diﬀerent models toresolve the long-standing mystery of their origin with the expected power of the detectors.
Our observations consist mainly of the energy spectrum, the primary mass composition,and the arrival directions of the energetic particles. The proposed models have their own
predictions that can be measurable by our detector. Let us show some examples. Figure
4.24 illustrates our typical discrimination power by measurement of the energy spectrum.
It is clearly seen that the spectrum is reconstructed well enough to show whether the GZK
cutoﬀ indeed exists or not.
The newly proposed scenarios such as the Top Down models and the neutrino Z-burst
model have predicted the “new” population of cosmic rays dominating above 1020 eV

106

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS
1026

dJ/dE E 3 [eV 2 / (m2 sr s)]

5 years running

10

25

10

24

10 23

10 20

10 19

10 21

Energy [eV]FIG. 4.24: 5 years observation of the energy spectrum by the Telescope Array. Closed circles
show the case if the spectrum simply extends well beyond 1020 eV [4] while open circles
represent the “standard model” with the GZK cutoﬀ assuming the sources are distributed
homogeneously in the Universe [17].
10

26

10

25

3

2

2

dJ/dE E [eV / (m sr s)]

5 years running

10 24

10

23

10 19

10 20

10

21

Energy [eV]FIG. 4.25: 5 years observation of the energy spectrum by the Telescope Array if the highest
energy cosmic ray has a new population dominating above 1020 eV as predicted by the Zburst or Top Down models. open circles represent the primary γ-ray component predictedby the Z-burst model [44].

4.8. DETECTION OF ACTIVE GALACTIC NUCLEI NEUTRINO

107

which would be created by decay of the supermassive particles [33] or cascading initiatedby superhigh energy astrophysical neutrino beams [45, 48]. In this case the Telescope
Array should see the new component extending well beyond 1020 eV. As illustrated inFig. 4.25, the observation for 5 years would be enough to detect these superhigh energy
particles that become predominant after the GZK cutoﬀ. The dip structure appears at
1020 eV if the low energy component presumably radiated from the radio galaxies, themost favorite candidates of the high energy cosmic ray emitters, exhibits the GZK cutoﬀ as
expected from our standard GZK picture. This would be a strong signature to suggest the
Top Down/Z-burst models that are necessarily associated with the hard energy spectrum(∼ E −2 ) extending to 1021 eV or even higher.
It should be noted that these models lead to primary γ-ray ﬂux that is comparable
or higher than nucleon intensity with energies above 1020 eV. As described in §4.6, ourcapability to measure the longitudinal shower proﬁle gives signiﬁcant sensitivity to identify
primary γ-rays if they exist. As shown in Fig. 4.25, our sensitivity would be good enoughto detect the predicted γ-rays component if these models are correct.
Because trajectories of γ-rays would not be bended by any magnetic ﬁeld, the mostenergetic particles are able to be traced back exactly to their emission point where one canﬁnd counterparts of the astronomical objects like AGNs or GRBs. Five years observationby the Telescope Array is expected to detect ∼ 250 events with energies greater than 1020
eV, and at least more than 30 % of them is predicted to be γ-rays. This indicates that
we will have a fairly good chance to see many triplets or more dense event clusters if thepossible small-scale anisotropy AGASA has seen is real. Whether we ﬁnd astronomical
counterparts in their directions and whether the counterparts are within the GZK horizon
or not would be direct evidence to identify the highest energy cosmic ray sources, which
resolves how the Universe produce such energetic particles, our long-standing astrophysicalpuzzle.

4.8

Detection of Active Galactic Nuclei Neutrino

In this section, we describe the potential to detect neutrinos of energies more than 1016 eVthrough deeply penetrating air showers using TA. Assuming some simple conservative trigger and selection requirements with a monocular detection technique which uses each detector station for air showers in an independent way, we obtain the acceptance for deeply
penetrating air showers as induced by high energy neutrinos by Monte Carlo method. Wethen give the expected event rates for two neutrino ﬂuxes as predicted in diﬀerent proton
AGN models.
Neutrinos produce showers in most interactions with the atmosphere which are of different nature depending on the process in consideration. We consider both deep inelastic
charged and neutral current interactions which always produce hadronic showers. In thecase of charged current electron neutrino interactions the emerging electron contributes in
addition a pure electromagnetic shower carrying a large fraction of the incoming particle
energy. We will ignore the resonant cross section because it is only signiﬁcant near the
peak of the cross section which occurs at an incoming neutrino energy of 6.4 PeV, well
below the region of high eﬃciency for the TA project.

108

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

For a neutrino ﬂux dIν /dEν interacting through a process with diﬀerential cross section
dσ/dy, where y is the fraction of the incident particle energy transferred to the target, theevent rate for deeply penetrating showers can be obtained by a simple convolution:

Rate[Esh > Eth ] = NA ρair

 ∞
Eth

dEsh

 1
0

dIν
dσ
(Eν ) (Eν , y) (Esh)
dEν
dy

dy

,

(4.34)

where NA is Avogadro’s number and ρair is the air density. The energy integral corresponds to the shower energy Esh which is related to the primary neutrino energy Eν in adiﬀerent way depending on the interaction being considered. is a detector acceptance,a function of shower energy, which corresponds to the volume and solid angle integrals
for diﬀerent shower positions and orientations with respect to the detector.The function is
diﬀerent for showers induced by charged current electron neutrino interactions from thosearising in neutral current or muon neutrino interactions. This is because hadronic andelectromagnetic showers have diﬀerences in the particle distributions functions, particularly for muons. For (νe + ν e )N charged current interactions, we take the shower energy to
be the sum of hadronic and electromagnetic energies, Esh = Eν . For (νμ + ν μ )N charged
current interactions and for neutral current interactions, we take the shower energy to be
the hadronic energy, Esh = yEν . To simplify the event rate evaluations, here we neglect(Eν , y) as a function of y replacing it into dσ(Eν , y = 0.2)δ(y − 0.2)
the distribution of dσdydy
in Eq. (4.34) because < y >∼0.2 does not depend on the primary energy beyond 1016 eV inboth cases of charged and neutral current interactions [112].
Assuming optimized eﬃciency for triggering on nearby as well as distant events as described in a later section on electronics and neglecting angular factor and Mie scattering
attenuation, an estimate of signal to noise generated in a time during which the track is inview of a PMT is given by:
Ne Nγ
S
=
N
4π



c
B

1/2
1/2 −r/λR 
e
D3
3/2

RP

d

,

where Ne is the number of electrons in the air shower generating the light, Nγ is theﬂuorescent yield which is measured to be ∼5 photons/electron/m, B is the night sky
background at new moon phase, which is measured to be ∼ 2 × 105 photons m−2 sr−1 μs−1
over the wave length range 310–440 nm including atmospheric airglow, RP RP is the impact
parameter, λR is the Rayleigh scattering length ∼ 18 km, is the overall optical eﬃciency
for converting photons into photoelectrons, d and D are the diameters of the PMT andmirror aperture respectively. Next, we convert electron size Ne to energy in order to obtainan estimate for energy triggering thresholds. We take [113]:
E = 1.6 × 10−9 Ne,

where E is the primary energy in EeV. Also assuming r = RP ,D = 3m, a crude estimate of the energy threshold is given by:−4

Eth [EeV] = 10





S
3/2
RP eRP /λRN,= 0.2, d = 0.06m, and4.8. DETECTION OF ACTIVE GALACTIC NUCLEI NEUTRINO

109

Eth(EeV)

where RP is in km. Eth as a function of RP in cases of S/N = 2 and 4 is shown in Fig. 4.26.
This simple estimate suggests that the sensitive TA detector optics and readout devices
should allow us the lower detectable energy threshold of 1016 eV and the more statistics for
AGN neutrino events because of the steep slope of the ﬂux spectrum shown in the previous
section. This is a good advantage of the TA detector. Furthermore realistic acceptanceestimates from Monte Carlo simulation study for neutrinos as a function of the primaryenergy will be described just later.

10

10

10

10

10

-1

-2

-3

-4

-5

0

2

4

6

8

10

12

14

16

18
20
Rp(km)

FIG. 4.26: A simple estimate of the minimum detectable energy in EeV as a function of
impact parameter RP in km in cases of PMT trigger levels S/N = 2 and 4.
Here we use new calculations of the cross sections for charged-current and neutral current
interactions of neutrinos with nucleons [114, 112], according to the CTEQ4-DIS (deepinelastic scattering) parton distributions [115]. The CTEQ4-DIS parton distributions takeaccount of new information about the parton distributions within the nucleon [116] using
more accurate and extensive DIS data than before from New Muon Collaboration (NMC)[117]and DESY ep collider HERA [118, 119], as well as new data from E665 [120]. The
cross section for the charged-current reaction νl N → l− + anything as a function of theneutrino energy Eν is shown in Fig. 4.27 (thin solid line). At low energies the chargedcurrent cross section σCC rises linearly with Eν . For energies exceeding about 104 GeV,
the cross section is damped by the W-boson propagator. Also Fig. 4.27 shows the neutralcurrent cross section σN C for the reaction νl N → νl +anything (dashed line), together with
σtot, the sum of charged-current and neutral-current cross sections (thick solid line). Since
the valence contribution is negligible Eν >106 GeV, νN and νN cross sections become
equal. For 1016 eV≤ Eν ≤1021 eV, the CTEQ4-DIS cross sections are given within 10% by:

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

σ(νN) [cm2]

110

10

10

-30

-31

νN total, CTEQ4-DIS
νN CC

10

10

10

10

10

10

10

-32

νN NC

-33

-34

-35

-36

-37

-38

10

10

10

11

10

12

10

13

10

14

10

15

10

16

10

17

10

18

10

19

10

20

10

21

Eν [eV]

log10(dI/dE [GeV-1cm-2s-1sr-1])

FIG. 4.27: Cross sections for interactions according to the CTEQ4-DIS parton distributions: dashed line σ(νl N → νl + anything) ; thin line, σ(νl N → l− + anything); thick line,
total (charged-current plus neutral-current) cross section.

-16

-18

-20

M

-22

-24

Total

-26

νe

-28

SZ-P

νμ
-30

-32

16

16.5

17

17.5

18

18.5
19
log10(E [eV])FIG. 4.28: Neutrino ﬂux predictions in the EeV range as labeled in the text.

4.8. DETECTION OF ACTIVE GALACTIC NUCLEI NEUTRINO−36

σCC (νN) = 5.5 × 10

−36

σN C (νN) = 2.3 × 10

2



cm

2



cm

σtot (νN) = 7.8 × 10−36 cm2



Eν
1GeV
Eν
1GeV

Eν
1GeV

111

0.363,
0.363,

0.363.

Detailed discussions on physics and ﬂux calculation of AGN neutrinos are in the previous
section. Here we select two typical models for neutrino production in AGN as shown in
Fig. 4.28. First model assumed chock acceleration in the AGN cores and predicted relatively
ﬂat ﬂuxes up to energies of about 1015 eV. For our event rate calculation we select theprediction of [77], labeled SZ-P. There is however recent evidence that the GeV to TeV
gamma ray emission observed from AGN corresponds to the blazar class. Most recent
models for the proton blazars site the acceleration in the jets themselves. We use theprediction of [78], labeled M, which illustrates that the emitted neutrinos may extend wellinto the EeV region.
The simulation methods employed to evaluate the detector acceptance and performancefor neutrino induced air showers are brieﬂy described here. A ten-eye ﬂuorescence systemlinearly arranged with 30km separation on a ﬂat place at 1600m above see level which issame as that of Utah site is investigated. Each eye (or detector station) images the skyfrom an elevation angle of 3◦ up to that of 35◦ with 1.2◦ diameter pixels. Other detailed
detector parameters are described in the previous section.
Each simulation for a given primary cosmic ray (electron neutrino, muon neutrino, or
proton) was performed at ﬁxed energy. The shower energy of neutrinos depends on thegeneration as described above. In the simulation we ﬁx the energy transfer parameter y to
be the average value < y >= 0.2, which is reasonable for Eν > 1016 eV . For each shower
energy, the mean depth of proton shower maximum was determined from simulations [121].
For each primary particle at each energy, the mean of the interaction length X1 was determined from the above interaction cross sections of neutrinos with nucleons or that ofprotons, 83.1(E/GeV)−0.052 g/cm2 [122]. The shower energy determines the shower size
at maximum, Nmax [86]. Given Nmax , Xmax , and X1 , the complete longitudinal proﬁlewas described by the Gaisser-Hillas function [113]. The NKG lateral distribution function[123, 124] normalized with the Gaisser parameterization has been used for the total numberof electrons and positrons in hadronic (electromagnetic) cascade showers to determine thelocation where ﬂuorescence lights are produced. We took into account the ﬂuctuations of
the ﬁrst interaction depth, impact point, and directional angles of air shower cores withappropriate distributions but not air shower size ﬂuctuations.
The light yield arriving at the detector site is calculated. Rayleigh and Mie scattering
processes are simulated, with full account taken of the spectral characteristics of the light.
The isotropically emitted ﬂuorescence light, as well as direct and scattered Cherenkov light,
is propagated. Night sky background noise is added to the signal. All processes that aﬀect

112

CHAPTER 4. PHYSICS SIMULATION AND EXPECTED RESULTS

3

log10(Acceptance [km w.eq. sr])

to overall optical eﬃciency; mirror area and reﬂectivity, optical ﬁlter transmission, PMT
quantum eﬃciency factors are folded with the light spectrum to give the photoelectron
yield in each PMT, due to signal and noise.
A “ﬁred” PMT is deﬁned to require that its instantaneous photoelectron current isgreater than the 2σ noise level of the night sky background. We preselected events if at
least one of 10 eyes contains at least 10 ﬁring PMTs. To ensure track quality, we cut
events of which shower maximums are not viewed by any eye. Finally to reject proton
background events, we selected only events with Xmax > 1300 g/cm2 . We obtained thedetector aperture corresponding the above selection cuts and calculated them into theacceptances multiplying the appropriate interaction length of neutrino with nucleon. The
results are shown in Fig. 4.29 for both electron and muon neutrinos as a function of the
primary energy.

3

νe

2.5

νμ
2

1.5

1

0.5

0

-0.5

16

16.5

17

17.5

18

18.5
19
log10(E [eV])FIG. 4.29: Acceptance of the TA detector to neutrino induced air shower. Volume units
are km3 of water equivalent. The higher, middle, and lower curves corresponds to events
after preselection, track quality, and proton rejection cuts.
We have estimated event rates for several energy threshold and selection cuts using avariety of models for the neutrino ﬂuxes from proton AGN models which assume the proton
acceleration region is at the core or the jets [77, 78].
The origins of the highest energy cosmic rays are not well understood, but cosmic rays
should be accompanied by very high energy neutrinos in all models. The absolute normalization and energy dependence of the ﬂuxes vary from model to model. The TA detector asa neutrino telescope ultimately will probe extraterrestrial accelerator sources using enoughstatistics of AGN neutrino events. Also we can distinguish between the assumptions forthe location in AGN where protons could be accelerated well from the observed neutrino
spectrum once we can detect neutrinos well with Eν >1016 eV.

Event Rate / Year4.8. DETECTION OF ACTIVE GALACTIC NUCLEI NEUTRINO

113

10 2

10

M
SZ-P

1

10

-1

16

16.5

17

17.5

18

18.5
19
log10(E [eV])FIG. 4.30: Annual event rates as a function of the neutrino energies in the TA detector forneutrino induced air showers with ﬂuxes from two diﬀerent AGN models (see text). Threekinds of curves from each proton AGN model correspond to the required selections.

Table 4.6: Annual event rates in the TA detector for neutrino induced air showers with
ﬂuxes from two diﬀerent AGN models (see text). Left and right side of slash(/) shows
the numbers of events which survive the cuts from proton AGN-jet and AGN-core model
respectively. The numbers of proton background events which survived all the cuts are also
shown.
Eth (eV) 10 PMTs (S/N ≥ 2) Viewing Xmax
1016
53.5 / 10.7
44.9 / 7.6
17
10
50.1 / 1.9
42.4 / 2.4

Xmax > 1300g/cm2
17.8 / 3.4
16.7 / 0.6

p background
310
17Chapter 5
Collaboration
The Telescope Array will be built by the collaboration of Japanese, American and Australian physicists. The group consists of cosmic ray physicists who have been working
in the AGASA and HiRes experiments, and high energy physicists who worked in large
accelerator experiments in US and Japan.
Table 5.1: List of Telescope Array Collaborators.
Institute
ICRR, Inst. for Cosmic Ray
Research, Univ. of Tokyo
KEK, High Energy Accelerator
Research Organization
Kinki Univ.
Konan Univ.
Nagasaki Inst. of Applied
Science
Osaka City Univ.
Saitama Univ.
Tokyo Inst. of Technology
Yamanashi Univ.
Columbia Univ.
Montana State Univ.
Rutgers Univ.
UCLA
Univ. of New Mexico
Univ. of Utah
Univ. of Adelaide

Participants
T.Aoki, M.Fukushima, N.Hayashida,
F.Ishikawa, H.Ohoka, M.Sasaki, M.Sasano,N.Takeda, M.Teshima, R.Torii, S.Yoshida
Y.Arai, S.Kabe, T.Suwada
M.ChikawaF.Kajino, M.Sakata, Y.Yamamoto
Y.Tanaka
S.Kawakami
N.Inoue
F.Kakimoto, S.Ogio
N.Kawasumi, K.Hashimoto, K.Honda
J.Boyer, B.Knapp, E.Mannel, M.Semen,
M.Shaevitz
J.Beltz
G.Thomson
K.Arisaka, D.Cline, W.Slater, A.Tripathi,
T.Vinogradova
B.D.Dieterle, G.Martin, J.A.J.Matthews,
S.Riley, M.Roberts, T.Tessier
Z.Cao, B.D.Kieda, E.C.Loh, J.N.Matthews,
P.Sokolsky, W.Springer, L.Wiencke
R.W.Clay, B.Dawson, N.Wild

115

Chapter 6
Cost and Schedule
The estimated total cost for the construction of Telescope Array is 8000 Million Japanese
Yen or 75.5 M$ (see Tab.6.1). The Japanese group will contribute 80% of the total cost.
The request of the construction budget was ﬁrst submitted to Monbusho in April 1999.
The US group plans to contribute to the rest of 20%. The request will be submitted to
DOE and NSF and will be reviewed by the SAGENAP committee.
Table 6.1: Estimated Cost of Telescope Array.
item
Telescope
Imaging camera
Electronics
Data acquisition
Atmosph. monitor
Infrastructure
Total

cost
(M Yen)
2370
2450
2120
230
300
530
8000

comments
mirror, frame, housing etc.
PMT, ﬁlter etc.
CSI, ADC, trigger, HVPS etc.
inc. oﬄine preprocessor
steerable laser, IR camera etc.
site, road, elect., communication etc.
= 75.5 M$ (1 $ = 106 Yen )We plan to test a complete set of telescope, electronics and atmospheric monitoring
system in 2000 near the planned site. All the R/D eﬀorts are targeted for the start ofconstruction in the spring of 2001. It will take 4 years to build 10 stations.

117

References[1] N. Hayashida et al., Phys. Rev. Lett.73, 3491 (1994).
[2] D. J. Bird et al., Astrophys.J. 441, 144 (1995).
[3] S. Yoshida et al., Astropart. Phys. 3, 105 (1995).
[4] M. Takeda et al., Phys. Rev. Lett. 81, 1163 (1998).
[5] K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G. T. Zatsepin and V. A. Kuzmin,
JETP Lett. 4, 178 (1966).
[6] The Pierre Auger Observatory Design Report (compilation by S. Swardy).
[7] P. O. Lagage and C. J. Cesarsky, Astronomy and Astrophys. 118, 223 (1983).
[8] D. B. Bird et al., Phys. Rev. Lett. 71, 3401 (1993).
[9] A. M. Hillas, in Proceedings of the 12th International Cosmic Ray Conference, Hobart,
Tasmania, Australia, 1971, Vol. 3, p. 1001.
[10] H. Y. Dai et al., J. Phys. G: Nucl. Phys. 14, 793 (1988).
[11] M. Takeda et al., Astrophys. J. 522, 225 (1999).
[12] N. Hayashida et al., in Proceedings of the 26th International Cosmic Ray Conference,
Salt Lake City, 1999, Vol. 3, p. 256. astro-ph/9906056.; N. Hayashida et al., Astrop.
Phys. 10, 303 (1999).
[13] T. Abu-Zayyad et al., astro-ph/9911144.
[14] N. Hayashida et al., J. Phys. G: Nucl. Part. Phys. 21, 1101 (1995).
[15] B. R. Dawson, R. Meyhandan and K. M. Simpson, Astropart. Phys. 9, 331 (1998).
[16] A. M. Hillas, Ann. Rev. Astron. Astrophys. 22, 425 (1984).
[17] S. Yoshida and M. Teshima, Prog. Theor. Phys. 89, 833 (1993).
[18] M. Simard-Normandin and P. P. Kronberg, Astrophys. J. 242, 74 (1980).
[19] R. J. Rand, S. Kulkarni and J. J. Hester, Astrophys. J. (Lett) 352, L1 (1990).
119

120

CHAPTER 6. COST AND SCHEDULE[20] R. J. Dettmar, Astronomy & Astrophysics 232, L15 (1990).
[21] P. P. Kronberg, Rep. Prog. Phys. 57, 325 (1994).
[22] L. Ferreti et al., Astronomy & Astrophysics 302, 680 (1994).
[23] E. Waxman, astro-ph/9911395.
[24] R. D. Blandford, asto-ph/9906026.
[25] P. L. Biermann, in Proceedings of Workshop on Observing Giant Cosmic Ray Air
Showers from ≥ 1020 eV Particles from Space, 1997, edited by J. F. Kirzmanic, J. F.
Ormes, and R. E. Streitmatter (AIP Conference Proc., 1997), 433, p. 22.
[26] C. A. Norman, D. B. Melrose and A. Achterberg, Astophys. J. 454, 60 (1995).
[27] F. C. Jones, in Proceedings of Workshop on Observing Giant Cosmic Ray Air Showers
from ≥ 1020 eV Particles from Space, 1997, edited by J. F. Kirzmanic, J. F. Ormes,
and R. E. Streitmatter (AIP Conference Proc., 1997), 433, p. 37.
[28] C. Cesarsky and V. Ptsukin, in Proceedings of the 23rd International Cosmic Ray
Conference, Calgary, 1993, Vol. 2, p. 341.
[29] A. V. Olinto, in Proceedings of the 23rd International Cosmic Ray Conference, Salt
Lake City, 1999, Vol. 4, p. 361.; astro-ph/9911154.
[30] R. V. E. Lovelace, Nature 262, 649 (1976).
[31] J. R. Jokipii and G. Morﬁll, Astrophys. J. 312, 170 (1987).
[32] T. Totani, Astropart. Phys. 11, 451 (1999).
[33] P. Bhattacharjee, C. T. Hill, and D. N. Schramm, Phys. Rev. Lett. 69, 567 (1992).
[34] G. Sigl, D. N. Schramm, and P. Bhattacharjee, Astropart. Phys. 2, 401 (1994).
[35] G. Sigl, D. N. Schramm, and P.Bhattacharjee, Science 270, 1977 (1995).
[36] G. Sigl, S. Lee, D. N. Schramm, and P. S. Coppi, Phys. Lett. B 392, 129 (1997).
[37] V. Berezinsky, P. Blasi, and A. Vilenkin, Phys. Rev. D 58, 103515 (1998).
[38] G. Sigl, S. Lee, P. Bhattacharjee, and S. Yoshida, Phys. Rev. D 59, 043504 (1999).
[39] C. T. Hill, Nucl. Phys. B 224, 469 (1983).
[40] V. Berezinsky, M. Kachelriess, and A. Vilenkin, Phys. Rev. Lett. 79, 4302 (1997).
[41] V. Kuzmin and I. Tkachev, Phys. Rev. D 59, 123006 (1999).
[42] D. J. H. Chung, E. W. Kolb and A. Riotto, Phys. Rev. Lett. 81, 4048 (1998).

121[43] K. Hamaguchi, Y. Nomura and T. Yanagida, Phys. Rev. D 58, 103503 (1998).
[44] S. Yoshida, G. Sigl, and S. Lee, Phys. Rev. Lett. 81, 5505 (1998).
[45] T. J. Weiler, Astropart. Phys. 11, 303 (1999).
[46] D. J. H. Chung, G. Farrar, E. Kolb, Phys. Rev. D 57, 4606 (1998); G. Farrar,
in Proceedings of Workshop on Observing Giant Cosmic Ray Air Showers from ≥1020 eV Particles from Space, 1997, edited by J. F. Kirzmanic, J. F. Ormes, and R.
E. Streitmatter (AIP Conference Proc., 1997), 433, p. 226.
[47] S. Coleman and S. L. Glashow, Phys. Rev. D 59, 116008 (1999).
[48] D. Fargion, B. Mele, and A. Salis, Astrophys. J. 517, 725 (1999).
[49] V. A. Kuzmin, and V. A. Rubakov, Phys. Atom. Nucl. 61, 1028 (1998).
[50] C. T. Hill and D. N. Schramm, Phys. Rev. D 31, 564 (1985).
[51] T. J. Weiler, Phys. Rev. Lett. 49, 234 (1982); Astrophys. J. 285, 495 (1984); E.
Roulet, Phys. Rev. D 47, 5247 (1993).
[52] S. Yoshida, Astropart. Phys. 2, 187 (1994).
[53] S. Yoshida, H. Dai, C. C. H. Jui, and P. Sommers, Astrophys. J. 479, 547 (1997).
[54] S. Lee, Phys. Rev. D 58, 043004 (1998).
[55] M. A. Lawrence, R. J. O. Reid, and A. A. Watson, J. Phys. G: Nucl. Part. Phys 17,733 (1991).
[56] W. Rhode et al., Astropart. Phys. 4, 217 (1996).
[57] R. M. Baltrusaitis et al., Phys. Rev. D 31, 2192 (1985).
[58] K. S. Capelle, J. W. Cronin, G. Parente, and E. Zas, Astropart. Phys. 8, 321 (1998).
[59] J. F. Ormes et al., in Proceedings of the 25th International Cosmic Ray Conference,
Durban, 1997, Vol. 5, P. 273.
[60] M. Jang and H. R. Miller, Astrophys. J. 452, 582 (1995).
[61] C. M. Urry and P. Padovani, Pub. Astr. Soc. Pacif. 107, 803 (1995).
[62] R. C. Hartman et al., Astrophys. J. Suppl. 123, 79 (1999).
[63] J. R. Mattox et al., Astrophys. J. xxx, xxx (1997).
[64] R. Mukherjee and J. Chiang, astro-ph/9902003.
[65] J. Chiang and R. Mukherjee, Astrophys. J. 496, 752 (1998).

122

CHAPTER 6. COST AND SCHEDULE[66] M. Catanese, Astrophys. J. 501, 616 (1998).
[67] M. Punch et al., Nature 358, 477 (1992).
[68] J. Quinn et al., Astrophys. J. 456, L83 (1995).
[69] Schubnell et al., astro-ph/9602068.
[70] M. J. Rees, Nature 211, 468 (1966).
[71] M. Sikora, M. C. Begelman, and M. J. Rees, Astrophys. J. Lett. 421, 153 (1994).
[72] R. J. Protheroe, astro-ph/9612213.
[73] K. Mannheim et al., astro-ph/9605107.
[74] R. J. Protheroe, ADP-AT-96-4.
[75] T. K. Gaisser, F. Halzen, and T. Stanev, Phys. Reports 258, 173 (1995).
[76] F. W. Stecker and M. H. Salamon, astro-ph/9501064.
[77] A. P. Szabo and R. J. Protheroe, in Proceedings of High Energy Neutrino Astrophysics
Workshop, U.Hawaii, March 1992, edited by V. J. Stenger, J. L. Learned, S. Pakvasa,
and X. Tata, (World Scienctiﬁc, 1993), p. 24.
[78] K. Mannheim, Astropart. Phys. 3, 295 (1995).
[79] F. Halzen and E. Zas, MADPH-97-982; astro-ph/9702193.
[80] P. Lipari, Astropart. Phys. 1, 195 (1993).
[81] L. Wiencke and S. Yoshida, TA Internal Report, TA-97-008 (1997).
[82] M. Kobayashi et al., Nucl. Inst. Meth. A 337, 355 (1992).
[83] M. V. Korzhik et al., Nucl. Inst. Meth. B B72, 499 (1992).
[84] S. Baccaro et al., Nucl. Inst. Meth. A 361, 209 (1995).
[85] N. Tsuchida et al., Nucl. Inst. Meth. A 385, 290 (1997).
[86] R. M. Baltrisaitis et al., Nucl. Instr. and Meth. A 240, 410 (1985).
[87] J. Boyer et al., in Proceedings of the 24th International Cosmic Ray Conference, ,1995, Vol. 3, p. 429.
[88] CASCADE (1996).
[89] S. Wotton, in Proceedings of CHEP-92, Annecy, France, 1992.
[90] F. Kakimoto et al., Nuclear Instruments and Methods, A 373, 572 (1996).

123[91] R. Gray et al., in Proceedings of the 26th International Cosmic Ray Conference, Salt
Lake City, 1999, Vol. 5, p. 353.
[92] M. Chikawa et al., in Proceedings of the 26th International Cosmic Ray Conference,
Salt Lake City, 1999, Vol. 5, p. 404.
[93] G. Martin and J. A. J. Matthews, Pierre Auger Note 99-037 / HiRes Note 10-11-1999(1999) available at http://www-hep.phys.unm.edu/∼johnm[94] F. X. Kneiays et al., Users Guide to Lowtran 7, Air Force Geophysics Laboratory,
AFGL-TR-88-0177, (also see http://www-vsbm.plh.af.mil/soft/modtran.html).
[95] D. R. Longtin, A Wind Dependent Desert Aerosol Model: Radiative Properties, Air
Force Geophysical Laboratory, AFGL-TR-88-0112, (1988).
[96] Ontar Corporation North Andover MA 01845-2000 USA, www.ontar.com.
[97] L. Wiencke et al., Nucl. Instr. Meth. A 428, 593 (1999).
[98] L. Wiencke et al., in Ultraviolet Atmospheric and Space Remote Sensing: Methods
and Instrumentation, edited by R. Huﬀman and K Dymond, Proc SPIE 3818, 59(1999).
[99] N. Hayashida et al., in Proceedings of the 26th International Cosmic Ray Conference,
Salt Lake City, 1999, Vol. 5, p. 357.
[100] DFM Enginnering Inc., Longmont CO USA. (www.sni.net/ dfm42/)[101] Big Sky Lasers Inc. Bozeman MT USA. (www.bigskylasers.com)[102] R. Ghandi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996);
Phys. Rev. D 58, 093009 (1998).
[103] B. L. Emerson, Ph.D Thesis, University of Utah (unpublished) (1992).
[104] L. D. Landau and I. J. Pomeranchuk, Dokl. Akad. Nauk. SSSR 92, 535 (1953).
[105] A. B. Migdal, Phys. Rev. 103, 1811 (1956).
[106] B. McBreen and C. J. Lambert, Phys. Rev. D 24, 2536 (1981).
[107] T. Stanev, and H. P. Vankov, Phys. Rev. D 55, 1365 (1997).
[108] S. J. Sciutto, GAP97-029 (1997).
[109] T. Erber, Rev. Mod. Phys. 38, 626 (1966).
[110] V. H. Bayer, B. M. Katkov, and V. S. Fadin, in Radiation of relativistic electrons(Moscow, Atomizdat, 1973).
[111] V. Anguelov and H. Vankov. No Identification

124

CHAPTER 6. COST AND SCHEDULE[112] R. Gandihi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5 81 (1995).
[113] T. K. Gaisser and A. M. Hillas, in Proceedings of the 15th International Cosmic Ray
Conference, Plovdiv, Bulgaria, 1977, Vol. 7, p. 353.
[114] R. Gandihi, C. Quigg, M. H. Reno, and I. Sarcevic, Phys. Rev. D 58, 093009 (1998).
[115] CTEQ Collaboration, H. L. Lai et al., Phys. Rev. D 55 1280 (1997).
[116] C. Quigg, “Neutrino Interaction Cross Sections”, FERMILAB-CONF-97/158-T.
[117] NMC, M. Arneodo et al., Phys. Lett. B 36 471 (1995).
[118] H1 Collaboration, S. Aid et al., Nucl. Phys. B 439 471 (1995); Nucl. Phys. B 470 3(1996).
[119] ZEUS Collboration, M. Derrick et al., Z. Phys. C 65 379 (1995).
[120] E665 Collaboration, M. R. Adams et al., Phys. Rev. D 54, 3006 (1996).
[121] T. K. Gaisser et al., Phys. Rev. D 47, 1919 (1993).
[122] M. Honda et al., Phys. Rev. Lett., 70, 525 (1993).
[123] K. Kamata and J. Nishimura, Prog. Theor. Phys. Suppl. 6, 93 (1958).
[124] K. Greisen, Prog. Cosmic Ray Physics 3, 1 (1956).