AbstractThe longitudinal development of an extensive air shower reaches its maximum at a depth, Xmax, that depends on the species of the primary cosmic ray. Using a technique based on Xmax, we measure the cosmic-ray mass composition from analyses of 3.7 years of monocular mode operations with the newly constructed fluorescence detectors of the Telescope Array experiment. The Xmax analysis shows our data to be consistent with a proton dominant composition at energies above 1018.0eV

Fujii, Toshihiro

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The Mass Composition of Ultra-high Energy Cosmic Rays Measured by New Fluorescence Detectors in the Telescope Array Experiment 

  Physics Procedia  61 ( 2015 )  418 – 424 
Available online at www.sciencedirect.com
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection and peer review is the responsibility of the Conference lead organizers, Frank Avignone, University of South Carolina, and Wick Haxton, 
University of California, Berkeley, and Lawrence Berkeley Laboratory
doi: 10.1016/j.phpro.2014.12.092 
ScienceDirect
The mass composition of ultra-high energy cosmic rays measured by
new fluorescence detectors in the Telescope Array experiment
Toshihiro Fujiia,b, for the Telescope Array Collaboration
aKavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois, 60637 USA
bInstitute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, 277-8582 JAPAN
Abstract
The longitudinal development of an extensive air shower reaches its maximum at a depth, Xmax, that depends on the species of the
primary cosmic ray. Using a technique based on Xmax, we measure the cosmic-ray mass composition from analyses of 3.7 years
of monocular mode operations with the newly constructed fluorescence detectors of the Telescope Array experiment. The Xmax
analysis shows our data to be consistent with a proton dominant composition at energies above 1018.0 eV.
c© 2011 Published by Elsevier Ltd.
Keywords: Mass composition; Ultra-high energy cosmic rays; Fluorescence detector; Telescope Array experiment
1. Introduction
Measurements of the mass composition and its energy dependence are essentially important for understanding
sources and propagations of cosmic rays and for constricting several theoretical models. Because of a low flux of
ultra-high-energy cosmic rays (UHECRs), the mass composition can not be measured directly. However, we can
make an indirect measurement via a technique using Xmax, which is the depth at which the longitudinal development
of an extensive air shower (EAS) reaches its maximum. The longitudinal shower development of a typical iron nucleus
with 56 nucleons, arriving with total energy E, is essentially the superposition of the longitudinal developments of 56
protons, each with energy E/56; the Xmax value for this shower will be smaller than that of a single proton with energy
E. The observed distribution of Xmax for cosmic rays at a given energy therefore depends on their mass composition.
Fluorescence detectors (FDs) observe atmospheric fluorescence photons emitted by molecules excited by an EAS,
providing a determination of the primary energy and the longitudinal shower development including Xmax. This
measurement has less dependence on simulations than other techniques, because the production and energy-loss
mechanisms of the EAS’s electromagnetic component (which make the dominant contribution to fluorescence photon
emissions) are less dependent on hadronic interaction models. The Telescope Array (TA) experiment is the largest
hybrid detector in the northern hemisphere continuing the eﬀort on understanding the origins of UHECRs [1]. TA
consists of 507 surface detectors (SDs) deployed on a square grid with 1.2 km spacing, covering an eﬀective area of
about 700 km2, and three FD stations outlook over the SD array. The full operation of TA began in March 2008.
One FD station, called “Middle Drum” (MD) and located northwest of the SD array, consists of 14 FD telescopes
previously used in the High Resolution Fly’s Eye (HiRes) experiment [2]. Two other stations at the array’s south-
east and southwest, respectively called “Black Rock Mesa” (BRM) and “Long Ridge” (LR), each consist of 12 FD
Email address: fujii@kicp.uchicago.edu (Toshihiro Fujii)
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection and peer review is the responsibility of the Conference lead organizers, Frank Avignone, University of South Carolina, 
and Wick Haxton, University of California, Berkeley, and Lawrence Berkeley Laboratory
 Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 419
Open Angle [deg]
0 2 4 6 8 10 12 14 16 18 20
En
tr
ie
s
0
200
400
600
800
1000
1200
Proton MC
Iron MC
(a) Arrival direction
]2  [g/cmTRUE - XmaxReco Xmax
-400 -300 -200 -100 0 100 200 300 400
En
tr
ie
s
0
200
400
600
800
1000
1200
1400
Proton MC
Iron MC
(b) Xmax
Figure 1. The resolutions of the arrival direction and the Xmax for EAS in the monocular mode analysis estimated by artificial data using primary
protons and irons with QGSJet-II-03 as the hadronic interaction model.
telescopes. The BRM and LR stations are newly designed and constructed for the TA experiment [3][4], with new
calibration [5][6] and atmospheric monitoring [7] systems.
2. Data analysis
We analyze data collected at the BRM and LR FD stations in a monocular mode, which is an analysis mode to
reconstruct an EAS to obtain primary particle’s properties using the measured shower image by one FD stations. Our
observation period is 3.7 years from January 2008 to September 2011. Using the Xmax distribution from our monocular
analysis, we obtain the mass composition of cosmic rays at energies above 1018.0 eV.
To reconstruct a geometry of an observed EAS, an arrival time ti of the signal in each photo-multiplier tube (PMT)
i is fitted by
ti = tcore +
1
c
sinΨ − sinαi
sin(Ψ + αi) r0 (1)
where αi is an angle formed by the i th PMT’s viewing direction and a direction vector from the FD station to the
shower core (shower axis’s impact point on the ground), Ψ is the angle on the shower detector plane formed by the
shower axis and the direction to the shower core, tcore is the time when the shower impacts the ground, and r0 is the
distance from the FD station to the shower core.
When the EAS geometry has been determined, the shower’s longitudinal development is calculated by the inverse
Monte Carlo method [10]. This inverse Monte Carlo technique iteratively explores the longitudinal-development
parameter space, searching for the optimum solution to reproduce the observed shower image. The geometries of
too faint or too short showers are diﬃcult to reconstruct accurately. Thus, we apply quality cuts to select only well-
reconstructed events in our analysis; the number of hit PMTs is larger than 10, the track length is larger than 10◦,
the time extent is larger than 2 μs and the depth of EAS maximum, Xmax, is within the station’s field of view, falling
between the first and the last depths (Xstart and Xend, respectively).
Since the EAS geometry is reconstructed using the arrival times at one FD station, the geometrical resolution is
not as precise as other analysis mode (such as stereo [8] or hybrid analysis [9]), and the reconstructed results may be
biased. Therefore, in the mass composition analysis, we apply additional strict cuts for a bias-free measurement of
Xmax in the monocular mode analysis. These cuts, which remove showers with biased geometry reconstruction or a
large contamination of the signal by ˇCherenkov photons, are similar to the “fiducial volume cuts” developed by the
Pierre Auger Observatory [11].
In order to cut the showers having geometries incoming to FD stations, we applied the following selection rules;
the minimum angle formed by a shower axis and a viewing direction from FD station must be larger than 20◦, the
420   Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 
(E (eV))
10
log
18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6
)2
<
X
m
ax
> 
(g/
cm
650
700
750
800
850
900
P QGSJetII-03 MC
P QGSJet01 MC
P SIBYLL 2.1 MC
Fe QGSJetII-03 MC
Fe QGSJet01 MC
Fe SIBYLL 2.1 MC
P QGSJetII-03 Reco.
P QGSJet01 Reco.
P SIBYLL 2.1 Reco.
Fe QGSJetII-03 Reco.
Fe QGSJet01 Reco.
Fe SIBYLL 2.1 Reco.
Figure 2. The averaged Xmax with primary protons (red) and irons (blue) without detector simulations and including them based on simulated
artificial events (pink and sky blue, respectively) with QGSJet01 (dotted line), QGSJet-II-03 (solid line) and SIBYLL 2.1 (dashed line).
angle of a shower axis within the shower-detector plane must be smaller than 90◦ and the Xstart must be larger than
150 g/cm2. In order to remove biased measurement on Xmax, the Xstart should be smaller than 700 g/cm2 , Xend should
be larger than 900 g/cm2 and the minimum distance from FDs to the shower axis defined as the impact parameter is
larger than 5 km. In this analysis, the selection criteria that we applied are independent of the primary cosmic-ray
energy, species and hadronic interaction model.
Before analyzing the observed data, we use Monte Carlo (MC) simulations to evaluate accuracies of the monocular
mode analysis and calculate expected distributions of Xmax in every energy bin under consideration. We use CORSIKA
[12] to simulate EAS developments for cosmic ray primary protons and irons, and for each species we used three
hadronic interaction models: QGSJet01, QGSJet-II-03 and SIBYLL 2.1. We generate artificial data based on the
CORSIKA showers applying the detector responses that were obtained in advance. These artificial data are also
processed with the identical method applied to the monocular mode analysis described above to obtain the distribution
of reconstructed Xmax values. The estimated resolutions for the arrival direction and Xmax for EAS with QGSJet-II-03
are shown in Figure 1. The resolutions of the arrival direction are 3.0 and 2.8 degree, and those of Xmax are 54.5 an
46.5 g/cm2 for primary protons and irons, respectively.
Figure 2 shows the averaged Xmax values calculated by CORSIKA as a function of primary energies for proton
and iron species with the three types of hadronic interaction models. The averaged Xmax diﬀerence between primary
protons and irons is 100 g/cm2, while the choice of interaction models makes the averaged Xmax a diﬀerence of up
to 30 g/cm2 at 1020 eV. The predicted Xmax for artificial events with the detector simulations and with established
reconstruction procedures is also shown in the same figure. There is only less than 10 g/cm2 diﬀerence between MC
rails and reconstructed ones for all species.
3. Results and discussion
Applying the reconstruction procedure and quality cuts to observed data with both BRM and LR stations during
3.7 years, we collect 1381 showers above 1018.0 eV. Before comparing the Xmax values from data to those of the
 Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 421
Figure 3. Distributions of the impact parameter (Rp), angle on the shower detector plane (Ψ), core location from the x-(south to north) and y-(west
to east) coordinates of the core location (Core X, Core Y), Xstart and Xend between observed data (black plot) and simulated expectations based on
primary protons (red histogram), and irons (blue histogram) with QGSJet-II-03.
(E (eV))
10
log
18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6
)2
<
X
m
ax
> 
(g/
cm
650
700
750
800
850
900
319
289
228
155
139
73
69
22
33
19
22
6
6
P QGSJetII-03
P QGSJet01
P SIBYLL 2.1
Fe QGSJetII-03
Fe QGSJet01
Fe SIBYLL 2.1
Data (TAUP2013 Preliminary)
 sys. uncert. 219 g/cm
Figure 4. The obtained averaged Xmax from data (black points), plotted with expectations estimated by the artificial simulations using primary
protons and irons with three hadronic interaction models (QGSJet01, QGSJet-II-03, SIBYLL 2.1). The color and style of each line has the same as
shown in Figure 2. The number of accepted showers in each energy bin is printed above that bin’s data point. The shaded area shows the systematic
uncertainty on Xmax, 19 g/cm2, for our monocular analysis.
422   Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 
]2Reconstructed Xmax [g/cm
400 500 600 700 800 900 1000 1100 1200
En
tr
ie
s
0
50
100
150
200
250
Data
MC Proton
MC Iron
MC Mixed
(a) 18.0 ≤ log(E) < 18.3
]2Reconstructed Xmax [g/cm
400 500 600 700 800 900 1000 1100 1200
En
tr
ie
s
0
10
20
30
40
50
60
70
80 Data
MC Proton
MC Iron
MC Mixed
(b) 18.3 ≤ log(E) < 18.6
]2Reconstructed Xmax [g/cm
400 500 600 700 800 900 1000 1100 1200
En
tr
ie
s
0
5
10
15
20
25
30
Data
MC Proton
MC Iron
MC Mixed
(c) 18.6 ≤ log(E) < 19.0
]2Reconstructed Xmax [g/cm
400 500 600 700 800 900 1000 1100 1200
En
tr
ie
s
0
1
2
3
4
5
6
7
Data
MC Proton
MC Iron
MC Mixed
(d) 19.0 ≤ log(E)
Figure 5. Reconstructed Xmax distributions in four energy range compared with simulated expectations based on artificial data using three energy-
independent compositions: purely proton (red), iron (blue) and the equal mixture of both (pink) with QGSJet-II-03.
 Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 423
item Energy Xmax
Fluorescence Yield 11% 5 g/cm2
Atmosphere 11% 12 g/cm2
Calibration 10% 5 g/cm2
Detector Geometry 4% 9 g/cm2
Reconstruction 10% 10 g/cm2
Total 21% 19 g/cm2
Table 1. The total systematic uncertainty of the energy scale and the Xmax in the monocular mode analysis.
artificial simulation data, we must confirm the reliability for our analysis by detailed comparisons between observed
data and simulated expectations. As shown in Figure 3, distributions of the impact parameter (Rp), angle on the
shower detector plane (Ψ), core location from the x-(south to north) and y-(west to east) coordinates of the core
location (Core X, Core Y), Xstart and Xend are in good agreement between observed data and simulated expectations.
Finally, we compare the observed averaged Xmax values with expected rails estimated from the artificial data using
primary protons or irons as shown in Figure 4. Xmax distributions for four energy regions are also shown in Figure 5.
The expected distributions for three diﬀerent mass compositions are shown for comparison: purely simulation proton,
iron and the equal mixture of both. Both Figure 4 and Figure 5 demonstrate that the observed Xmax values indicate a
proton dominant composition above 1018.0 eV. The systematic uncertainty of our energy scale of FD reconstruction
is 21%, and that of Xmax is 19 g/cm2 for our monocular analysis. In the systematic errors we take into account
fluorescence yields, atmospheric conditions, detector calibrations and geometries and reconstructions as shown in
table 1.
4. Conclusions
The newly constructed FDs for the TA experiment have been taking steady measurements of UHECRs since early
2008. From the monocular mode analysis for 3.7 year data observed at the BRM and LR stations, we have measured
the mass composition of cosmic rays with energies above 1018.0 eV using the Xmax technique described above. The
obtained averaged Xmax and its distributions indicate a proton dominant composition at energies above 1018.0 eV.
5. Acknowledgements
The Telescope Array experiment is supported by the Japan Society for the Promotion of Science through Grants-
in-Aid for Scientific Research on Specially Promoted Research (21000002) “Extreme Phenomena in the Universe
Explored by Highest Energy Cosmic Rays”, and the Inter-University Research Program of the Institute for Cosmic
Ray Research; by the U.S. National Science Foundation awards PHY-0307098, PHY-0601915, PHY-0703893, PHY-
0758342, PHY-0848320, PHY-1069280, and PHY-1069286 (Utah) and PHY-0649681 (Rutgers); by the National
Research Foundation of Korea (2006-0050031, 2007-0056005, 2007-0093860, 2010-0011378, 2010-0028071, R32-
10130); by the Russian Academy of Sciences, RFBR grants 10-02-01406a and 11-02-01528a (INR), IISN project
No. 4.4509.10 and Belgian Science Policy under IUAP VI/11 (ULB). The foundations of Dr. Ezekiel R. and Edna
Wattis Dumke, Willard L. Eccles and the George S. and Dolores Dore Eccles all helped with generous donations. The
State of Utah supported the project through its Economic Development Board, and the University of Utah through the
Oﬃce of the Vice President for Research. The experimental site became available through the cooperation of the Utah
School and Institutional Trust Lands Administration (SITLA), U.S. Bureau of Land Management and the U.S. Air
Force. We also wish to thank the people and the oﬃcials of Millard County, Utah, for their steadfast and warm
support. We gratefully acknowledge the contributions from the technical staﬀs of our home institutions as well as the
University of Utah Center for High Performance Computing (CHPC). This work was supported by Grand-in-Aid for
the Japan Society for the Promotion of Science (JSPS) Fellowship for Research Abroad.
424   Toshihiro Fujii /  Physics Procedia  61 ( 2015 )  418 – 424 
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The Mass Composition of Ultra-high Energy Cosmic Rays Measured by New Fluorescence Detectors in the Telescope Array Experiment

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