Acta Polytechnica


doi:10.14311/AP.2013.53.0728
Acta Polytechnica 53(Supplement):728–731, 2013 © Czech Technical University in Prague, 2013

available online at http://ojs.cvut.cz/ojs/index.php/ap

DETECTION OF A CHANGE OF SLOPE IN THE SPECTRUM OF
HEAVY MASS COSMIC RAYS PRIMARIES BY THE

KASCADE-GRANDE EXPERIMENT

A. Chiavassaa,∗, W.D. Apelb, J.C. Arteaga-Velázquezc, K. Bekkb,
M. Bertainaa, J. Blümerb,d, H. Bozdogb, I.M. Brancuse, E. Cantonia,f,

F. Cossavellad,l, K. Daumillerb, V. de Souzag, F. Di Pierroa, P. Dollb,
R. Engelb, J. Englerb, M. Fingerd, B. Fuchsd, D. Fuhrmannh,

F. Garinod, H.J. Gilsb, R. Glasstetterh, C. Grupeni, A. Haungsb,
D. Heckb, J.R. Hörandelj, D. Huberd, T. Huegeb, K.-H. Kamperth,

D. Kangd, H.O. Klagesb, K. Linkd, P. Łuczakk, M. Ludwigd,
H.J. Mathesb, H.J. Mayerb, M. Melissasd, J. Milkeb, B. Mitricae,
C. Morellof, J. Oehlschlägerb, S. Ostapchenkoa,m, N. Palmierid,

M. Petcue, T. Pierogb, H. Rebelb, M. Rothb, H. Schielerb, S. Schood,
F.G. Schröderb, O. Simal, G. Tomae, G.C. Trincherof, H. Ulrichb,

A. Weindlb, J. Wocheleb, M. Wommerb, J. Zabierowskik

a Dipartimento di Fisica, Università degli Studi di Torino, Italy
b Institut für Kernphysik, KIT – Karlsruher Institut für Technologie, Germany
c Universidad Michoacana, Instituto de Física y Matemáticas, Morelia, Mexico
d Institut für Experimentelle Kernphysik, KIT – Karlsruher Institut für Technologie, Germany
e National Institute of Physics and Nuclear Engineering, Bucharest, Romania
f Osservatorio Astrofisico di Torino, INAF Torino, Italy
g Universidade São Paulo, Instituto de Física de São Carlos, Brasil
h Fachbereich Physik, Universität Wuppertal, Germany
i Department of Physics, Siegen University, Germany
j Dept. of Astrophysics, Radboud University Nijmegen, The Netherlands
k National Centre for Nuclear Research, Department of Cosmic Ray Physics, Lodz, Poland
l Department of Physics, University of Bucharest, Bucharest, Romania
m now at: Max-Planck-Institut für Physik, München, Germany
n now at: University of Trondheim, Norway
∗ corresponding author: andrea.chiavassa@to.infn.it

Abstract. KASCADE-Grande is an extensive air shower experiment devoted to the study of cosmic
rays in the 1016 ÷ 1018 eV energy range. The array comprises various detectors allowing independent
measurements of the number of muons (Nµ) and charged particles (Nch) of extensive air showers (EAS).
These two observables are then used to study the primary energy spectrum, separating the events
into two samples on the basis of the shower size ratio, corrected for attenuation in the atmosphere,
ln Nµ/ ln Nch. The two samples represent the light and heavy mass groups of the primaries. In the
studied energy range, only the spectrum of heavy primaries shows a significant change of slope. The
energy (estimated using the QGSJET II hadronic interaction model) of this feature is in agreement
with the expectations of a rigidity-dependent knee feature.

Keywords: cosmic rays, energy spectrum, extensive air showers.

728

http://dx.doi.org/10.14311/AP.2013.53.0728
http://ojs.cvut.cz/ojs/index.php/ap


vol. 53 supplement/2013 Detection of a Change of Slope in the Spectrum

1. Introduction
Knee-like structures have been found in the spectrum
of the light and medium components of cosmic rays
in the 1015 ÷ 1017 eV energy range [1]. These kinks
produce the overall feature in the all-particle cosmic
ray spectrum known as the knee, which was discovered
by Kulikov and Khristiansen more than fifty years
ago [2]. Several hypotheses have been proposed ot
explain the origin of this feature [3–5]. A first class of
models attributes this spectral feature to astrophysical
mechanisms. The most favoured scenario explains
this radiation by galactic sources (e.g. Super Novae
Remnants) and the spectral feature of the knee either
by the limit of acceleration in galactic sources or by the
limit of containment inside local magnetic fields. Both
scenarios predict the knee of the primary spectrum
at an energy in agreement with the measured energy
and scaling, for different elements, with the atomic
number. Alternative scenarios explain the knee by
a change of the hadronic interactions originating the
extensive air showers; these models predict an energy
dependence of the knee on the primaries mass number.
Both kinds of models predict that there should also
be a knee-like structure in the energy spectrum of the
heavy component of cosmic rays at about 1017 eV.

Experiments that have studied the knee in the last
decade have focused on the 1014÷1016 eV energy range,
and have therefore not been able to detect the change
in the slope of heavy primaries. The KASCADE-
Grande experiment was designed to address the prob-
lem of the iron-knee by studying cosmic rays in the
1016 ÷ 1018 eV energy range [6].

Measurements of the primary spectrum of at least
two mass groups can only be obtained if the experi-
ment has a high resolution for all the EAS components
needed to reach this goal. In KASCADE-Grande, the
observables used are the muon (Nµ) and charged par-
ticles (Nch, defined as the sum of the electrons and
muons in the shower) numbers in the EAS at detec-
tion level. The ratio between the number of muons
and charged particles has been identified as a variable
with enough resolution to separate (with less than
10 % contaminations) the two event samples.

The technique is briefly described and the results
are presented. The energy scale of the results depends
on the hadronic interaction model used in the EAS
simulations (e.g. QGSJET II [7]), while the spectral
features are always detected in the electron-poor event
sample (e.g. a high value of the above-mentioned ratio)
irrespective of the exact value used to separate the
events.

2. The KASCADE-Grande
experiment

The KASCADE-Grande detector is located on the
North Campus of the Karlsruhe Institute of Technol-
ogy, Germany (110 m a.s.l.). Two arrays are the main

y
 c

o
o

r
d

in
a

t
e

 [
m

]

x coordinate [m]

Grande stations

KASCADE

MTD

CD

Figure 1. Experimental layout of the KASCADE-
Grande experiment.

components of the experiment. The layout is shown
in Fig. 1.

The first detector, called Grande, is 700 × 700 m2 in
area and uses 37 × 10 m2 plastic scintillator detectors
to sample the charged particle density at different
distances from the EAS core. These measurements
are used to estimate Nch, the EAS arrival direction
and core location. The second detector, i.e. the former
KASCADE experiment array, comprises a 252 e/γ
unshielded liquid scintillator and shielded µ plastic
scintillation detectors. This array, covering a smaller
(200 × 200 m2) surface, independently measures the
muon number Nµ.

A complete description of the event reconstruction
and of the achieved experimental resolutions can be
found in [6]. In this short note, it is important to
point out that Nch and Nµ are detected with 15 %
resolution and 25 % resolution, respectively.

3. Analysis and Results
The analysis was performed on a particular subset
of data with zenith angles (θ) below 40°, with recon-
structed cores in a fiducial area of 1.52 × 105 m2 inside
the central region of Grande and with shower sizes
log Nch > 6.0 and log Nµ > 5.0. For these selection
criteria, full trigger and reconstruction efficiency is
achieved at an energy of log(E/GeV) ≥ 7.4. The
present analysis is based on 1173 days of data taking,
for an exposure of 2 × 1013 m2 s sr.
The analysis technique is described in detail in [8].

Using the Constant Intensity Cut method (CIC, de-
scribed in [9]), the attenuation curves of Nch and Nµ
in the atmosphere are obtained, and can be used to
calculate the equivalent particle numbers at a refer-
ence zenith angle (θref = 21.5°, selected as the mean

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Andrea Chiavassa et al. Acta Polytechnica

(E/GeV)
10

log
7 7.5 8 8.5 9

Y

0.7

0.75

0.8

0.85

0.9

Fe

H

He

C

Si

0.84

Figure 2. Mean values of Y CIC for five primaries
(from bottom to top: H, He, C, Si, Fe) vs. primary
energy. Error bars represent the RMS of the Y CIC
distributions.

value of the events zenith angle distribution). The CIC
method allows the EAS propagation in the atmosphere
to be taken into account in a model-independent way.
Having converted the measured Nch(θ) and Nµ(θ)

to the values at the reference angle, the ratio

Y CIC =
ln Nµ(θref)
ln Nch(θref)

(1)

is calculated. The values of the ratio Y CIC for differ-
ent primaries is then investigated using a full shower
and detector simulation (sampling the primary energy
on a power-law spectrum between 1015 and 1018 eV).
The mean value of Y CIC is almost energy-independent,
and it increases with the mass of the primary nucleus,
as shown in Fig. 2 (for a QGSJET II based simulation).
Selecting events with Y CIC ≥ 0.84, we separate the
electron-poor and electron-rich (Y CIC < 0.84) samples.
Heavy elements (Si and Fe) are representatives of the
first group, and light elements (H and He) are repre-
sentatives of the second. The fraction of misclassified
events for protons and iron nuclei is lower than 15 %
for energies above full efficiency, and does not depend
on the reconstructed energy.

The primary energy (log(E/GeV)) is attributed to
each event following a procedure based on the Nch
and Nµ observables that is described in detail in [8].
The measured spectra of the light and heavy mass
groups are shown in Fig. 3. It can easily be observed
that the spectrum of the heavy component shows a
clear knee-like structure [8]. Fitting the spectrum
with a broken power-law expression [8], the change of
the spectral slope is Δγ = −0.48 from γ1 = 2.76 ±
0.02 to γ2 = 3.24 ± 0.05, with the break position at
log(E/GeV) = 7.92 ± 0.04. The statistical significance
of this change of slope is 3.5σ. However it should be
pointed out that the light component of cosmic rays
is still present at energies between 1017 and 1018 eV,
though its relative abundance is smaller than that of
the heavy component.

7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9

1
.7

 s
r 

s
 e

V
2

 /
 m

2
.7

 E
⋅

d
J
/d

E
 

19
10

20
10

(E/GeV)
10

log

All particle spectrum

Y<0.84

Y>0.84

Figure 3. Reconstructed energy spectrum of the
electron-poor and electron-rich components together
with the all-particle spectrum for the angular range
0° < θ < 40°. The error bars show the statistical
uncertainties.

4. Conclusions
Applying a cut based on the ratio between the muon
and charged particles numbers (calculated at a refer-
ence zenith angle), the KASCADE-Grande experiment
is able (due to its unprecedented resolution in this en-
ergy range) to separate the measured events in samples
generated by light and heavy primaries. The energy
spectra of both components was measured; the energy
spectrum of the heavy mass group shows a knee-like
feature at an energy of ∼ log(E/GeV) = 7.92 ± 0.04.
This primary energy value depends heavily on the
hadronic interaction model used for the shower simu-
lation, e.g. QGSJET II; while the knee-like structure
in the spectrum is detected for different cut values
of Y CIC (i.e. different hadronic interaction models).
The spectral steepening occurs at an energy where the
charge-dependent knee of primary iron is expected,
when the knee at about 3 ÷ 5 × 1015 eV is assumed to
be caused by a decrease in the flux of primary protons
and/or Helium nuclei.

Acknowledgements
The authors would like to thank the members of the en-
gineering and technical staff of the KASCADE-Grande
collaboration, who have contributed to the success of the
experiment. The KASCADE-Grande experiment is sup-
ported by the BMBF of Germany, the MIUR and INAF
of Italy, the Polish Ministry of Science and Higher Educa-
tion, and the Romanian Authority for Scientific Research
UEFISCDI (PNII-IDEI grants 271/2011 and 17/2011).

References
[1] Apel W. D. et al. (KASCADE collaboration): 2005,
Astropart. Phys. 24, 1

[2] Kulikov G. V., Khristiansen G. B.: 1959, Sov. Phys.
JETP 35, 441

[3] Hörandel J. R.: 2004, Astropart. Phys. 21, 241–265

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[4] Peters B.: 1961, Il Nuovo Cimento 22, 800. Binns
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[5] Ptsukin V. S. et al.: 1993, Astron. Astrophys. 268,
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[6] Apel W. D. et al. (KASCADE-Grande collaboration):
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[7] Ostapchenko S. S.: 2006, Nucl. Phys. B (Proc. Suppl.)
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[8] Apel W. D. et al. (KASCADE-Grande collaboration):
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[9] Kang D. et al. (KASCADE-Grande collaboration):
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Arteaga-Velázquez J. C. et al. (KASCADE-Grande
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	Acta Polytechnica 53(Supplement):728–731, 2013
	1 Introduction
	2 The KASCADE-Grande experiment
	3 Analysis and Results
	4 Conclusions
	Acknowledgements
	References