29 July 2021
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Latest results from the KASCADE-Grande experiment
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DOI:10.1016/j.nima.2013.11.045
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The definitive version is available at:
Latest results from the KASCADE-Grande experiment
A. Chiavassac, W.D. Apela, J.C. Arteaga-Vel´azquezb, K. Bekka, M. Bertainac, J. Bl¨umera,d, H. Bozdoga, I.M. Brancuse,
E. Cantonic,f,1, F. Cossavellad,2, C. Curcioc, K. Daumillera, V. de Souzag, F. Di Pierroc, P. Dolla, R. Engela, J. Englera, B. Fuchsd,
D. Fuhrmannh,3, H.J. Gilsa, R. Glasstetterh, C. Grupeni, A. Haungsa, D. Hecka, J.R. H¨orandelj, D. Huberd, T. Huegea,
K.-H. Kamperth, D. Kangd, H.O. Klagesa, K. Linkd, P. Łuczakk, M. Ludwigd, H.J. Mathesa, H.J. Mayera, M. Melissasd, J. Milkea,
B. Mitricae, C. Morellof, J. Oehlschl¨agera, S. Ostapchenkoa,4, N. Palmierid, M. Petcue, T. Pieroga, H. Rebela, M. Rotha,
H. Schielera, S. Schooa, F.G. Schr¨odera, O. Simal, G. Tomae, G.C. Trincherof, H. Ulricha, A. Weindla, J. Wochelea, J. Zabierowskik aInstitut f¨ur Kernphysik, KIT - Karlsruher Institut f¨ur Technologie, Germany
bUniversidad Michoacana, Instituto de F´ısica y Matem´aticas, Morelia, Mexico cDipartimento di Fisica, Universit`a degli Studi di Torino, Italy
dInstitut f¨ur Experimentelle Kernphysik, KIT - Karlsruher Institut f¨ur Technologie, Germany eNational Institute of Physics and Nuclear Engineering, Bucharest, Romania
fOsservatorio Astrofisico di Torino, INAF Torino, Italy gUniversidade S˜ao Paulo, Instituto de F´ısica de S˜ao Carlos, Brasil
hFachbereich Physik, Universit¨at Wuppertal, Germany iDepartment of Physics, Siegen University, Germany jDept. of Astrophysics, Radboud University Nijmegen, The Netherlands kNational Centre for Nuclear Research, Department of Cosmic Ray Physics, Lodz, Poland
lDepartment of Physics, University of Bucharest, Bucharest, Romania
Abstract
The KASCADE-Grande experiment operated at KIT from January 2004 to November 2012, measuring EAS generated by primary cosmic rays in the 1016−1018eV energy range. The experiment detected, for each single event, with a high resolution, the total
number of charged particles (Nch) and of muons (Nµ).
In this contribution we present the latest results about:
(i) the measurement of the all particle energy spectrum, discussing the influence of the hadronic interaction model used to derive the energy calibration of the experimental data.
(ii) The energy spectra derived separating the events according to the Nµ/Nch ratio. This technique allowed us to unveil a steepening of the spectrum of heavy primaries at E ∼ 1016.92±0.04eV and a hardening of the spectrum of light primaries at E ∼
1017.08±0.08eV.
(iii) The elemental spectra (for five mass groups) obtained applying a detailed unfolding analysis technique. (iv) A search for large scale anisotropies.
Keywords: Cosmic Rays, Extensive Air Showers, Knee, Spectra
1. Introduction 1
Measurements of the cosmic-rays all-particle and individual
2
elemental spectra, of the primary chemical composition and
3
of the anisotropies in the primaries arrival directions are the
4
tools to understand the phenomenology of cosmic rays. The
5
KASCADE-Grande experiment was built to investigate the
en-6
ergy range from 1016to 1018eV with the main goal of searching
7
for a change of slope in the primary spectrum of the heavy
par-8
ticles and to investigate the possible transition from a galactic
9
to an extra-galactic origin of cosmic rays in this energy range.
10
The results obtained at lower energies by KASCADE[1] and
11
EAS-TOP[2] as well as by other experiments suggest that the
12
Email address: [email protected] (A. Chiavassa)
1now at: Istituto Nazionale di Ricerca Metrologia, INRIM, Torino. 2now at: DLR Oberpfaffenhofen, Germany.
3now at: University of Duisburg-Essen, Duisburg, Germany. 4now at: University of Trondheim, Norway.
knee in the primary energy spectrum observed at 3 − 4 × 1015eV
13
is due to a break in the spectrum of light elements (Z≤ 6).
14
Several models foresee a rigidity dependence of such breaks.
15
Therefore, a knee of the heavy component is expected around
16
1017eV. Such features can only be investigated by precise
mea-17
surements both of the all-particle spectrum (i.e. the spectrum
18
of the entire event sample) and of the spectra of different mass
19
groups (i.e. the spectra of event samples obtained applying a
20
primary mass dependent selection).
21
The evolution with energy of the primary chemical
compo-22
sition brings also relevant informations concerning the
transi-23
tion from a galactic origin of the primary radiation to an
extra-24
galactic one. Most of the astrophysical models identify in a
25
change toward a composition dominated by light (mainly
pro-26
tons) primaries a sign of such a transition. It is therefore of
27
main importance to perform composition studies in a wide
en-28
ergy range and with high resolution.
29
In addition a search for large scale anisotropies in the arrival
30
directions of cosmic rays is performed, that is an observable
31
very sensible to the propagation of the primaries in the galactic
32
magnetic fields. The foreseen effect is very low (of the order of
33
10−3−10−2) and is hidden by counting differences induced by
34
pressure and temperature variations. To take into account such
35
effects we have performed the search following the East-West
36
method[3].
37
In this contribution we will present the updated results
ob-38
tained for the all-particle[4], light[5] and heavy[6] primary
en-39
ergy spectra; we will discuss the elemental spectra obtained
un-40
folding the Nch−Nµspectrum[7]; and we will show the upper 41
limits derived from a search for large scale anisotropies[8].
42
2. Experimental setup 43
The multi-detector experiment KASCADE[9] (located at
44
49.1◦ n, 8.4◦ e, 110m a.s.l.) was extended to
KASCADE-45
Grande in 2003 by installing a large array of 37 stations
con-46
sisting of 10m2scintillation detectors each, the layout is shown
47
in figure 1. KASCADE-Grande[10] provides an area of 0.5km2
48
and operates jointly with the existing KASCADE detectors.
49
The joint measurements with the KASCADE muon tracking
50
devices are ensured by an additional cluster (Piccolo) located
51
close to the center of KASCADE-Grande and deployed for fast
52
trigger purposes. For results of the muon tracking devices see
53
[11].
54
The Grande detectors are sensitive to charged particles, while
55
the KASCADE array detectors measure the electromagnetic
56
component and the muonic component separately. These muon
57
detectors enable to reconstruct the total number of muons on an
58
event-by-event basis also for Grande triggered events.
59
Basic shower observables like the core position,
angle-of-60
incidence, and total number of charged particles (Nch) are
pro-61
vided by the measurements of the Grande stations. The Grande
62
array accuracy in the EAS parameters reconstruction is
mea-63
sured comparing, on an event by event basis, the values
inde-64
pendently determined by the KASCADE and by the Grande
ar-65
rays. A resolution of 5m on the core position, of 0.7◦ on the
66
arrival direction, and of 15% on the total number of charged
67
particles (with a systematic difference lower than 5%) has been
68
achieved. The total number of muons is determined using
69
the core position reconstructed by the Grande array and the
70
muon densities measured by the KASCADE muon array
de-71
tectors. The resolution on the NµEAS parameter is evaluated
72
reconstructing simulated events, a ∼ 20% accuracy has been
73
achieved. More details on the experimental setup and on the
74
event reconstruction can be found in[10].
75
Full efficiency for triggering and reconstruction of
air-76
showers is reached at a primary energy of 1016eV, slightly
vary-77
ing on the cuts needed for the reconstruction of the different
78 observables[10]. 79 X coordinate (m) -600 -500 -400 -300 -200 -100 0 100 -700 -600 -500 -400 -300 -200 -100 0 100 KASCADE Array Grande Stations Y coordinat e (m)
Figure 1: Layout of the KASCADE-Grande experiment. The KASCADE array and the distribution of the 37 stations of the Grande array are shown. The 192 muon detectors are placed in the outer 12 clusters of the KASCADE array (hatched area). The dashed line shows the fiducial area selected for the all-particle and heavy mass group spectra analysis. The dotted line indicates the area used for the measurement of the light mass group spectrum.
3. Results 80
3.1. All particle energy spectrum 81
The energy of the primary particle that originated the
de-82
tected EAS is determined by the KASCADE-Grande
experi-83
ment by means of the Nch and Nµobservables[4], combining
84
these two variables indeed we can lower the dependence from
85
the chemical composition of the primary particles. This is
ob-86
tained evaluating for each event the so called k parameter, that
87
is essentially a measurement of the ratio between the muon and
88
the charged particles numbers.
89
k = log10(Nch/Nµ) − log10(Nch/Nµ)H log10(Nch/Nµ)Fe−log10(Nch/Nµ)H
(1)
90
log10(Nch/Nµ)H,Fe= cH,Felog10Nch+ dH,Fe (2)
91
From its definition is clear that k is a number centered around
92
zero (one) for proton (iron) generated events, if expressed as a
93
function of Nchfor Monte Carlo events, assuming intermediate
94
values for all other primaries. The values of the k parameters
95
are tuned by a full EAS and detector simulation, the analysis
re-96
ported in [4] is based on the QGSJetII-02[12] hadronic
interac-97
tion model. Having calculated, for each event, the k parameter
98
the primary energy is estimated from the Nchvalue:
99
log10(E/GeV) = [aH+ (aFe−aH) · k] log10(Nch) +
bH+ (bFe−bH) · k (3) 2
16 10 1017 18 10 )-1 -2.918 E x I/(A -0.8 -0.6 -0.4 -0.2 0 0.2 0.4
primary energy [eV] KASCADE-Grande
Figure 2: The all-particle energy spectrum obtained with KASCADE-Grande. The residual intensity after multiplying the spectrum with a factor of E2.918is displayed as well as the band of systematic uncertainty.
To take into account the shower evolution in atmosphere
100
the parameters, aH,Fe,bH,Fe,cH,Fe,dH,Fe, contained in the k and
101
E expressions are derived in five different angular intervals, 102
whose upper limits are: 16.7◦,24.0◦,29.9◦,35.1◦ and 40.0◦.
103
The values of the parameters can be found in[4].
104
The all-particle energy spectrum is then measured in the five
105
different angular bins. As shown in[4] these spectra are slightly
106
shifted, indicating that the EAS evolution in atmosphere is not
107
correctly described by the simulations. Nevertheless these
dif-108
ferences are inside the experimental uncertainties and thus we
109
mediate them to obtain the all particle energy spectrum
mea-110
sured in zenith angle range from 0◦ to 40◦. The residuals of
111
the all-particle energy spectrum multiplied by a factor, in such
112
a way that the middle part of the spectrum becomes flat are
113
shown in figure 2.
114
The measured spectrum cannot be described by a single
115
power law: a hardening around 1016eV and a steepening at
116
log10(E/eV) = 16.92 ± 0.10 are observed. The statistical
signif-117
icance of the steepening is 2.1σ, here the change of the spectral
118
slope is from γ = −2.95 ± 0.05 to γ = −3.24 ± 0.08. The
119
same spectral features are meanwhile confirmed by the
Tunka-120
133[13] and Ice-Top[14] experiments.
121
This procedure relies on the EAS simulation and thus
de-122
pends on the high-energy hadronic interaction model used.
123
To evaluate the systematic effects introduced in the
all-124
particle spectrum measurement[15] the same procedure has
125
been repeated using events simulated with the SIBYLL2.1[16],
126
EPOS1.99[17] and QGSJetII-04[18] hadronic interaction
mod-127
els.
128
Applying the energy calibration functions, obtained by each
129
model, to the measured data the all-particle energy spectra for
130
the five zenith angle bins are obtained for the four previously
131
mentioned models; for all of them, except QGSJetII-04, an
un-132
folding procedure has been applied. Different sources of
un-133
certainty affect the all-particle energy spectrum. A detailed
134
description is reported in[4]. They take into account: a) the
135
angular dependence of the parameters appearing in the energy
136
calibration functions of the different angular ranges. b) The
137
possible bias introduced in the energy spectrum by different
pri-138
mary compositions. c) The spectral slope of Monte Carlo used
139
in the simulations. d) The reconstruction quality of Nch and
140
Nµ. The total systematic uncertainty is ∼ 20% at the threshold
141
(E = 1016eV) and ∼ 30% at the highest energies (E = 1018eV)
142
almost independently from the interaction model used to
inter-143
pret the data. The final all-particle spectrum of
KASCADE-144
Grande is obtained (see figure 3) by combining the spectra for
145
the individual angular ranges. Only those events are taken into
146
account, for which the reconstructed energy is above the energy
147
threshold for the angular bin of interest. In general the shape of
148
the energy spectrum is very similar for all models, however, a
149
shift in flux is clearly observed which amounts to ∼ 25%
in-150
crease in case of SIBYLL2.1 and ∼ 10% decrease in case of
151
EPOS1.99. This is the consequence of the energy shift assigned
152
on an event-by-event basis. This result gives an estimation of
153
the systematic uncertainty on the experimental flux due to the
154
hadronic interaction model used to interpret the data, and it is
155
essentially independent of the technique used to derive the flux,
156
namely averaging the fluxes obtained in different angular bins.
157
The shift in the assigned energy to the data is also visible in the
158
hardening around ∼ 2 × 1016eV and in the steepening around
159
1017eV which look shifted among the models in general
agree-160
ment with the energy shift. This result indicates that the features
161
seen in the spectrum are not an artifact of the hadronic
interac-162
tion model used to interpret the data but they are in the
mea-163
sured data. In the overlapping region, KASCADE-Grande data
164
are compatible inside the systematic uncertainties with
KAS-165
CADE data interpreted with the same model.
166
3.2. Energy spectra of individual mass groups 167
The k parameter previously defined can also be used to
sep-168
arate the events in samples generated by two different primary
169
mass groups. To emphasize the features of the heavy elements
170
we selected the electron-poor events with kep(E) ≥ (kC(E) +
171
kS i(E))/2, i.e. events with a k value greater that the mean
172
value of the expectations for C and Si primaries
(QGSJetII-173
02[12] based simulation). The spectra of these event samples
174
are shown in figure 4, the band indicates changes of the spectra
175
when the cut is varied by one standard deviation in the kep(E)
176
definition.
177
The reconstructed spectrum of the electron-poor events
178
shows a distinct knee like feature at about 8 × 1016eV.
Apply-179
ing a fit of two power laws to the spectrum interconnected by a
180
smooth knee[19] results in a statistical significance of 3.5σ that
181
the entire spectrum cannot be described with a single
power-182
law. The change of the spectral index is ∆γ = −0.48 ± 0.05
183
from γ = −2.76 ± 0.02 to γ = −3.24 ± 0.05 with the break
184
position at log10(E/eV) = 16.92 ± 0.04. The spectrum of the
185
electron-rich events (corresponding, with this cut definition, to
186
light and medium mass primaries) is compatible with a single
187
power law with slope index γ = −3.18 ± 0.01. A recovery to a
188
harder spectrum at energies greater than 1017eV cannot be
ex-189
cluded by this analysis.
190
To increase the statistics and deeply investigate this
possi-191
ble hardening of the light primaries spectrum a larger fiducial
192
Energy (eV/particle) 16 10 1017 1018 ) 1.5 eV -1 sr -1 sec -2 J(E) (m 2.5 dI/dE x E 15 10 16 10 17 10 Akeno (J.Phys.G18(1992)423) AGASA (ICRC 2003) HiResI (PRL100(2008)101101) HiResII (PRL100(2008)101101) Yakutsk (NewJ.Phys11(2008)065008) AUGER (ICRC 2009) EAS-TOP (Astrop.Phys.10(1999)1) TIBET-III (ApJ678(2008)1165) GAMMA (J.Phys.G35(2008)115201) TUNKA (Nucl.Phys.B,Proc.Sup.165(2007)74) KASCADE (QGSJET01 Astrop.Phys.24(2005)1) KASCADE (SIBYLL2.1 Astrop.Phys.24(2005)1) KASCADE (QGSJET II, M.Finger 2011) KASCADE (EPOS1.99, M.Finger 2011) µ KASCADE-Grande (QGSJET II) Nch-N
µ KASCADE-Grande (SIBYLL 2.1) Nch-N µ KASCADE-Grande (EPOS 1.99) Nch-N (RAW) µ KASCADE-Grande (QGSJET II-04) Nch-N
Figure 3: Comparison of the all-particle energy spectrum obtained with KASCADE-Grande data based on SIBYLL2.1 (blue), QGSJetII-02 (black), QGSJetII-04 (pink) and EPOS1.99 (red) models to results of other experiments. The band denotes the systematic uncertainties in the flux estimation
electron-rich sample all-particle (104489 events) electron-poor sample 1020 dI/dE x E 2 .7 (m -2 sr -1 s -1 eV 1 .7 ) log10(E/eV) 16 16.5 17 17.5 18 = -2.95±0.05 = -3.24±0.08 = -2.76±0.02 = -3.24±0.05 KASCADE-Grande = -3.18±0.01 10 eV17 10 eV18 1019
Figure 4: Reconstructed energy spectrum of the poor and electron-rich components together with the all-particle spectrum for the angular range 0◦
−40◦
. The error bars show the statistical uncertainties; the bands assign systematic uncertainties due to selection of the subsamples.
area has been defined, essentially accepting events at larger
dis-193
tances from the muon detector (i.e. from the KASCADE array,
194
see figure 1). The main effect of this event selection is that
195
the 100% efficiency is reached at higher energies, that is not
196
a problem for this analysis aimed to study a possible spectral
197
feature at energies greater than 1017eV. In order to emphasize
198
features of the light mass group we redefine the cut on the k
199
parameter as ker(E) ≤ (kC(He) + kC(E))/2 (again a simulation
200
based on the QGSJetII-02 hadronic interaction model is used).
201
The obtained spectrum is shown in figure 5; a hardening, or
202
ankle-like feature, is clearly observed. Fitting this spectrum
203
with the same function used for the all-particle and heavy mass
204
groups primary spectra we obtain a change of the spectral
in-205
dex from γ = −3.25 ± 0.05 to γ = −2.79 ± 0.08 at an energy of
206
log10(E/eV) = 17.08 ± 0.08. The measured number of events
207
above the bending is Nmeas = 595. Without the bending we 208
would expect Nexp = 467 events above this ankle-like feature. 209
The Poisson probability to measure at least Nmeasevents above
210
the bending, if Nexp are expected is P ∼ 7.23 × 10−9,
corre-211
sponding to a 5.8σ significance.
212
Comparing the two previous observations it is important to
213
notice that the knee in the heavy component occurs at a lower
214
energy compared to the bending in the spectrum of the light
215
primaries. Therefore the steepening of the heavy spectrum and
216
the recovery of the light component are not due to a bias in the
217
reconstruction or separation procedures. It is worth pointing out
218
that the slope of the heavy mass spectrum above the knee-like
219
feature is very similar to the slope of the light mass spectrum
220
before the ankle-like feature. The slope index of the light mass
221
group spectrum above the ankle-like feature is γ ∼ −2.7 and
222
this can be interpreted as an indication of an injection of a new
223
(extragalactic) population of high energy cosmic-rays[5].
224
3.3. Energy spectra for elemental groups by unfolding analysis 225
The measured two-dimensional shower size spectrum of the
226
number of charged particles (log10(Nch)) vs. the number of
227
muons (log10(Nµ)) is the basis for the unfolding analysis[1] to
228
(E/eV) 10 log 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 ) 1.7 eV -1 s -1 sr -2 (m 2.7 dI/dE x E 19 10
light (sep. between He-CNO) band of systematic uncertainty
0.08 ± /eV) = 17.08 break, light (E 10 0.08, log ± = -2.79 2 γ 0.05, ± = -3.25 1 γ 2506 1487 882 539 322 195 144 92 55 43 40 18 8
Figure 5: The reconstructed energy spectrum of the light mass component of cosmic rays. The number of events per energy bin is indicated as well as the range of systematic uncertainty. The error bars show the statistical uncertain-ties.
infer the absolute fluxes of different mass groups. With the
229
KASCADE-Grande resolution we can separate five different
230
groups. Only events with shower sizes for which the
exper-231
iment is fully efficient are considered, i.e. log10(Nch) ≥ 6.0
232
and log10(Nµ) ≥ 5.0. In order to avoid effects due to the
vary-233
ing attenuation of the shower sizes for different angles of
in-234
cidence, the data set used is restricted to showers with zenith
235
angles θ ≤ 18◦.
236
The analysis objective is to compute the energy spectra of
237
five cosmic ray mass groups[7](represented by protons (p),
238
helium (He), carbon (C), silicon (Si), and iron (Fe) nuclei)
239
from 1016eV to 1017eV primary energies. The convolution
240
of the sought-after differential fluxes dJn/d log10E of the
pri-241
mary cosmic ray nuclei n into the measured number of
show-242
ers Nicontributing to the cell i of shower size plane, and thus
243
to the content of this specific charged particle and muon
num-244
ber bin (log10(Nch); log10(Nµ)) in the previously mentioned
bi-245
dimensional spectra, can be described by an integral equation:
246 Ni= 2πAfTm Nnucl X n=1 Z 18◦ 0◦ Z +∞ −∞ dJn d log10E
pn sinθ cosθ d log10E dθ (4)
One has to sum over all Nnucl elements contributing to the
247
all-particle cosmic ray spectrum, in this analysis the five
repre-248
sentative primaries. Tmis the measurement time, the factor 2π
249
accounts for the integration over the azimuth angle, and Af is
250
the chosen fiducial area. The term pnrepresents the conditional
251
probability to reconstruct a certain combination of charged
par-252
ticle and muon number respectively (i.e. to get an entry in the
253
cell (log10(Nch); log10(Nµ)) if the air shower inducing particle
254
was of the type n and had an energy E.
255
In figure 6, the unfolded differential energy spectra of lighter
256
primaries (protons as well as helium and carbon nuclei, upper
257
panel), and the spectra of heavier ones (silicon and iron
nu-258
clei, lower panel) are depicted. In addition, all five unfolded
259
spectra are summed up to the all-particle flux, which is also
260
shown. The shaded band indicates the methodical
uncertain-261
ties, while the error bars represent the statistical error
origi-262
nating from the limited measurement time. The uncertainties
263
due to the interaction models used, i.e. of QGSJET-II-02 and
264
FLUKA2002.4[20], cannot be considered.
265
With increasing energy the heavy component gets the
dom-266
inant contributor to the cosmic ray composition. The spectra
267
of lighter primaries are rather featureless within the given
un-268
certainties, while in the iron spectrum there is a slight bending
269
discernible at around 1017eV. The position of this knee-like
270
structure agrees with those observed in the all-particle and in
271
the heavy component spectra previously discussed.
272
There are no indications so far that the interaction models
273
used, i.e. QGSJET-II-02 and FLUKA 2002.4, have serious
274
deficits in the description of the physics of hadronic interactions
275
at these energies, which, however, does not mean necessarily
276
that these models must be accurate in all details. Different
in-277
teraction models primarily have impact on the absolute scale of
278
energy and masses, such that model uncertainties can shift the
279
unfolded spectra, possibly resulting in different abundances of
280
the primaries, while specific structures, e.g. knee-like features
281
of the spectra, are less affected by the models.
282
3.4. Large Scale Anisotropies 283
The search for large scale anisotropies has been performed
284
through a differential method, the so called East-West[3]
285
method, based on the counting rate differences between
East-286
ward and West-ward directions. This method allows to remove
287
counting rate variations caused by atmospheric and
instrumen-288
tal effects. The used data set contains 107 events recorded
be-289
tween December 2003 and October 2011. To ensure
recon-290
struction quality, a cut on the zenith angle θ and on the
num-291
ber of charged particles at observation level (Nch) was applied:
292
θ <40◦and Log(Nch) > 5.2.
293
Figure 7 shows the modulation in sidereal5 time obtained
294
using the East-West method. The amplitude of the first
har-295
monic calculated in sidereal time is (0.28 ± 0.08) × 10−2 with
296
a 0.2% Rayleigh probability of being due to background
fluc-297
tuation (i.e. σ = 3.5) at median energy 3.3 × 1015eV. The 298
99% C.L. upper limit on the amplitude is 0.47 × 10−2, derived
299
according to the distribution drawn from a population
charac-300
terized by an anisotropy of unknown amplitude and phase as
301
derived by Linsley[21].
302
To investigate a variation of the amplitude and phase of the
303
first harmonic with primary energy we have performed the same
304
analysis in intervals of the number of charged particles. In order
305
to have bins containing events of similar energy and have good
306
statistics in each of them we have chosen ∆LogNch= 0.4. The 307
results are shown in table 1, in none of the bins the amplitude
308
of the harmonic is statistically significant and so we have
calcu-309
lated the upper limits at 99% confidence level. The Nchlimits
310
5sidereal time: Common time scale among astronomers which is based on the Earth’s rotation measured relative to the fixed stars.
of the intervals used for the harmonic analysis are converted to
311
primary energy and the median energy of the events in each bin
312
is defined as representative energy.
313
log10(Nch) E (PeV) Asid×10−2 hours 5.2-5.6 2.6 × 1015 0.26 ± 0.10 15 ± 1.4 5.6-6 5.5 × 1015 0.39 ± 0.17 16.3 ± 1.6
6.0-6.4 1.2 × 1016 0.67 ± 0.41 8.4 ± 2.2 6.4-6.8 2.5 × 1016 0.5 ± 1.0 18.4 ± 6.6
>6.8 6.3 × 1016 4.6 ± 2.2 16.1 ± 1.8 log10(Nch) E (PeV) U.L. 10−2 P % 5.2-5.6 2.6 × 1015 0.49 3
5.6-6 5.5 × 1015 0.77 7
6.0-6.4 1.2 × 1016 1.54 26
6.4-6.8 2.5 × 1016 2.8 85
>6.8 6.3 × 1016 9.3 11
Table 1: Results of harmonic analysis through the East-West method for five intervals of Nch.
4. Conclusions 314
The KASCADE-Grande experiment took data from January
315
2004 to end 2012, detecting EAS generated by primary cosmic
316
rays in the 1016−1018eV energy range. In this contribution we
317
have shown the main results obtained so far by the experiment:
318
1. a measurement of the all-particle energy spectrum,
show-319
ing that it cannot be described by a single slope power
320
law. A hardening slightly above 1016eV and a steepening 321
at log10(E/eV) = 16.92 ± 0.10 are detected.
322
2. The measurement of the light and heavy primary mass
323
group energy spectra. These spectra were obtained
di-324
viding the events in two samples on the basis of the ratio
325
between the muon and the charged particles numbers. A
326
steepening at log10(E/eV) = 16.92 ± 0.04 in the spectrum
327
of the electron poor event sample (heavy primaries) and
328
a hardening at log10(E/eV) = 17.08 ± 0.08 in the one of
329
the electron rich (light primaries) one were observed. The
330
slope of the heavy mass group spectrum above the
knee-331
like feature is similar to the one of the light mass spectrum
332
before the the ankle-like feature.
333
3. Applying the unfolding algorithm to the NchvsNµspectrum
334
we could extract the spectra of five different elemental
335
mass groups. These measurement relies on the hadronic
336
interaction model utilized in the EAS simulation.
Mak-337
ing use of the same hadronic interaction model to interpret
338
the data, the measured fluxes are in agreement with those
339
obtained at lower energies by the KASCADE array and
340
with the findings above for the KASCADE-Grande energy
341
range.
342
4. Upper limits on the amplitude of large scale anisotropies
343
in four Nchbins.
344
Acknowledgment:The authors would like to thank the mem-345
bers of the engineering and technical staff of the
KASCADE-346
Grande collaboration, who contributed to the success of the
ex-347
periment. The KASCADE-Grande experiment is supported in
348
Germany by the BMBF and by the Helmholtz Alliance for
As-349
troparticle Physics - HAP funded by the Initiative and
Network-350
ing Fund of the Helmholtz Association, by the MIUR and INAF
351
of Italy, the Polish Ministry of Science and Higher Education,
352
and the Romanian Authority for Scientific Research UEFISCDI
353
(PNII-IDEI grants 271/2011 and 17/2011).
354
References 355
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(E/GeV) 10 primary energy in log
7 7.2 7.4 7.6 7.8 8 8.2 ) 1 .5 0 G e V -1 s -1 s r -2 / (m 2 .5 0 E d if. fl u x d J /d E · 10 2 10 3 10 sum spectrum p He C (E/GeV) 10 primary energy in log
7 7.2 7.4 7.6 7.8 8 8.2 ) 1 .5 0 G e V -1 s -1 s r -2 / (m 2 .5 0 E d if. fl u x d J /d E · 10 2 10 3 10 sum spectrum Si Fe
Figure 6: The unfolded energy spectra for elemental groups of cosmic rays, represented by protons, helium, and carbon nuclei (upper panel) as well as by silicon and iron nuclei (lower panel), based on KASCADE-Grande measure-ments. The all-particle spectrum that is the sum of all five individual spectra is also shown. The error bars represent the statistical uncertainties, while the error bands mark the maximal range of systematic uncertainties. The response matrix used is based on the interaction models QGSJetII-02[12] and FLUKA 2002.4[20]
Figure 7: Sidereal time distribution of the number of counts (θ < 40◦
and
LogNch>5.2) in 20 minutes intervals obtained applying the East-West method. The dashed line shows the calculated first harmonic.
