All-particle cosmic ray energy spectrum measured with 26 IceTop stations

Abstract

We report on a measurement of the cosmic ray energy spectrum with the IceTop
air shower array, the surface component of the IceCube Neutrino Observatory at
the South Pole. The data used in this analysis were taken between June and
October, 2007, with 26 surface stations operational at that time, corresponding
to about one third of the final array. The fiducial area used in this analysis
was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV
measured for three different zenith angle ranges between 0{\deg} and 46{\deg}.
Because of the isotropy of cosmic rays in this energy range the spectra from
all zenith angle intervals have to agree. The cosmic-ray energy spectrum was
determined under different assumptions on the primary mass composition. Good
agreement of spectra in the three zenith angle ranges was found for the
assumption of pure proton and a simple two-component model. For zenith angles
{\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the
cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on
composition assumption. Spectral indices above the knee range from -3.08 to
-3.11 depending on primary mass composition assumption. Moreover, an indication
of a flattening of the spectrum above 22 PeV were observed.

Full text

Page 1

All-particle cosmic ray energy spectrum measured with 26 IceTop
stations
R. Abbasiab, Y. Abdouw, T. Abu-Zayyadah, M. Ackermannap, J. Adamsp, J. A. Aguilarv,
M. Ahlersab, D. Altmanna, K. Andeenab, J. Auffenbergab, X. Baiaf,1, M. Bakerab,
S. W. Barwickx, V. Baumac, R. Bayg, J. L. Bazo Albaap, K. Beattieh, J. J. Beattyr,s, S. Bechetm,
J. K. Beckerj, K.-H. Beckerao, M. Bellam, M. L. Benabderrahmaneap, S. BenZviab,
J. Berdermannap, P. Berghausaf, D. Berleyq, E. Bernardiniap, D. Bertrandm, D. Z. Bessonz,
D. Bindigao, M. Bissoka, E. Blaufussq, J. Blumenthala, D. J. Boersmaa, C. Bohmai, D. Bosen,
S. Böserk, O. Botneran, L. Brayeurn, A. M. Brownp, S. Buitinkn, K. S. Caballero-Moraam,
M. Carsonw, M. Casiern, D. Chirkinab, B. Christyq, F. Clevermannt, S. Coheny,
D. F. Cowenam,al, A. H. Cruz Silvaap, M. V. D’Agostinog, M. Danningerai, J. Daughheteee,
J. C. Davisr, C. De Clercqn, T. Degnerk, F. Descampsw, P. Desiatiab, G. de Vries-Uiterweerdw,
T. DeYoungam, J. C. Díaz-Vélezab, J. Dreyerj, J. P. Dummab, M. Dunkmanam, J. Eischab,
R. W. Ellsworthq, O. Engdegårdan, S. Eulera, P. A. Evensonaf, O. Fadiranab, A. R. Fazelyf,
A. Fedynitchj, J. Feintzeigab, T. Feuselsw, K. Filimonovg, C. Finleyai, T. Fischer-Waselsao,
S. Flisai, A. Franckowiakk, R. Frankeap, T. K. Gaisseraf, J. Gallagheraa, L. Gerhardth,g,
L. Gladstoneab, T. Glüsenkampap, A. Goldschmidth, J. A. Goodmanq, D. Góraap, D. Grantu,
A. Großae, S. Grullonab, M. Gurtnerao, C. Hah,g, A. Haj Ismailw, A. Hallgrenan, F. Halzenab,
K. Hanap, K. Hansonm, P. Heimanna, D. Heinena, K. Helbingao, R. Hellauerq, S. Hickfordp,
G. C. Hillb, K. D. Hoffmanq, B. Hoffmanna, A. Homeierk, K. Hoshinaab, W. Huelsnitzq,2,
P. O. Hulthai, K. Hultqvistai, S. Hussainaf, A. Ishiharao, E. Jacobiap, J. Jacobsenab,
G. S. Japaridzed, H. Johanssonai, A. Kappesi, T. Kargao, A. Karleab, J. Kirylukaj, F. Kislatap,∗,
S. R. Kleinh,g, S. Klepserap, J.-H. Köhnet, G. Kohnenad, H. Kolanoskii, L. Köpkeac, S. Kopperao,
D. J. Koskinenam, M. Kowalskik, M. Krasbergab, G. Krollac, J. Kunnenn, N. Kurahashiab,
T. Kuwabaraaf, M. Labaren, K. Laihema, H. Landsmanab, M. J. Larsonam, R. Lauerap,
J. Lünemannac, J. Madsenah, R. Maruyamaab, K. Maseo, H. S. Matish, K. Meagherq,
M. Merckab, P. Mészárosal,am, T. Meuresm, S. Miareckih,g, E. Middellap, N. Milket, J. Milleran,
T. Montaruliv,3, R. Morseab, S. M. Movital, R. Nahnhauerap, J. W. Namx, U. Naumannao,
S. C. Nowickiu, D. R. Nygrenh, S. Odrowskiae, A. Olivasq, M. Olivoj, A. O’Murchadhaab,
S. Panknink, L. Paula, C. Pérez de los Herosan, D. Pielotht, J. Posseltao, P. B. Priceg,
G. T. Przybylskih, K. Rawlinsc, P. Redlq, E. Resconiae, W. Rhodet, M. Ribordyy, M. Richmanq,
B. Riedelab, J. P. Rodriguesab, F. Rothmaierac, C. Rottr, T. Ruhet, D. Rutledgeam,
B. Ruzybayevaf, D. Ryckboschw, H.-G. Sanderac, M. Santanderab, S. Sarkarag, K. Schattoac,
M. Scheela, T. Schmidtq, S. Schönebergj, A. Schönwaldap, A. Schukrafta, L. Schultek,
A. Schultesao, O. Schulzae, M. Schuncka, D. Seckelaf, B. Semburgao, S. H. Seoai, Y. Sestayoae,
S. Seunarinel, A. Silvestrix, M. W. E. Smitham, G. M. Spiczakah, C. Spieringap, M. Stamatikosr,4,
T. Stanevaf, T. Stezelbergerh, R. G. Stokstadh, A. Stößlap, E. A. Strahlern, R. Ströman,
M. Stüerk, G. W. Sullivanq, H. Taavolaan, I. Taboadae, A. Tamburroaf, S. Ter-Antonyanf,
S. Tilavaf, P. A. Toaleak, S. Toscanoab, D. Tosiap, N. van Eijndhovenn, A. Van Overloopw,
J. van Santenab, M. Vehringa, M. Vogek, C. Walckai, T. Waldenmaieri, M. Wallraffa,
M. Walterap, R. Wassermanam, Ch. Weaverab, C. Wendtab, S. Westerhoffab, N. Whitehornab,
K. Wiebeac, C. H. Wiebuscha, D. R. Williamsak, R. Wischnewskiap, H. Wissingq, M. Wolfai,
T. R. Woodu, K. Woschnaggg, C. Xuaf, D. L. Xuak, X. W. Xuf, J. P. Yanezap, G. Yodhx,
S. Yoshidao, P. Zarzhitskyak, M. Zollai
aIII. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
bSchool of Chemistry & Physics, University of Adelaide, Adelaide SA, 5005 Australia
cDept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508,
USA
dCTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA
eSchool of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332,
USA
fDept. of Physics, Southern University, Baton Rouge, LA 70813, USA
gDept. of Physics, University of California, Berkeley, CA 94720, USA
hLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
iInstitut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
jFakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
1
arXiv:1202.3039v1 [astro-ph.HE] 14 Feb 2012

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kPhysikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany
lDept. of Physics, University of the West Indies, Cave Hill Campus, Bridgetown BB11000, Barbados
mUniversité Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
nVrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
oDept. of Physics, Chiba University, Chiba 263-8522, Japan
pDept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
qDept. of Physics, University of Maryland, College Park, MD 20742, USA
rDept. of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH
43210, USA
sDept. of Astronomy, Ohio State University, Columbus, OH 43210, USA
tDept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
uDept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
vDépartement de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
wDept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
xDept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA
yLaboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland
zDept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA
aaDept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA
abDept. of Physics, University of Wisconsin, Madison, WI 53706, USA
acInstitute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
adUniversité de Mons, 7000 Mons, Belgium
aeT.U. Munich, D-85748 Garching, Germany
afBartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE
19716, USA
agDept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
ahDept. of Physics, University of Wisconsin, River Falls, WI 54022, USA
aiOskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden
ajDepartment of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
akDept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA
alDept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA
amDept. of Physics, Pennsylvania State University, University Park, PA 16802, USA
anDept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
aoDept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
apDESY, D-15735 Zeuthen, Germany
Abstract
We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array,
the surface component of the IceCube Neutrino Observatory at the South Pole. The data used
in this analysis were taken between June and October, 2007, with 26 surface stations operational
at that time, corresponding to about one third of the final array. The fiducial area used in this
analysis was 0.122km2. The analysis investigated the energy spectrum from 1 to 100PeV measured
for three different zenith angle ranges between 0◦and 46◦. Because of the isotropy of cosmic rays
in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray
energy spectrum was determined under different assumptions on the primary mass composition.
Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure
proton and a simple two-component model. For zenith angles θ < 30◦, where the mass dependence
is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32PeV,
depending on composition assumption. Spectral indices above the knee range from −3.08 to −3.11
depending on primary mass composition assumption. Moreover, an indication of a flattening of
the spectrum above 22PeV were observed.
Keywords:
cosmic rays, energy spectrum, IceCube, IceTop
Preprint submitted to Astroparticle PhysicsFebruary 15, 2012

Page 3

1. Introduction
Almost 100 years after the discovery of cosmic rays, their sources and acceleration mechanisms
still remain mostly unknown. The energy spectrum of cosmic rays as measured by various exper-
iments follows a relatively smooth power law with spectral index γ ≈ −2.7 up to about 4PeV,
where it steepens to γ ≈ −3.1 [1]. While this feature in the spectrum called “knee” is well es-
tablished, its origin remains controversial [2]. Most models to explain the knee involve a change
in chemical composition of cosmic rays in the energy region above the knee. Such a change has
been observed by various experiments [3] but systematic uncertainties are too large to discriminate
individual descriptions. Features in the all-particle cosmic ray energy spectrum and their chemical
composition bear important information on the acceleration and propagation of cosmic rays. The
measurement of the cosmic ray energy spectrum and composition is the main goal of the IceTop
air shower array.
IceTop is the surface component of the IceCube Neutrino Observatory at the geographic South
Pole. Installation of IceCube and IceTop was completed at the end of 2010, with 86 IceCube strings
and 81 IceTop stations deployed covering an area of about 1km2and a volume of about 1km3.
IceTop was designed to measure the energy spectrum and the primary mass composition of cosmic
ray air showers in the energy range between 5 · 1014eV and 1018eV.
The average atmospheric depth at the South Pole is about 680g/cm2. IceTop is therefore
located close to the shower maximum for showers in the PeV range (for vertical protons about
550g/cm2at 1PeV to 720g/cm2at 1EeV). This has the advantage that local shower density
fluctuations are smaller than at later stages of shower development.
In this paper, we present the first analysis of IceTop data on high-energy cosmic rays and a
measurement of the cosmic ray energy spectrum. This analysis is based on air shower data taken
with the IceTop surface stations. The data were taken between June and October 2007 with 26
IceTop stations operating, which comprise about 1/3 of the complete detector.
Section 2 of this paper gives an overview over the IceTop array, and the processing and cal-
ibration of tank signals, which are the basis for reconstructing air showers. Section 3 describes
the dataset and run selection criteria. Section 4 introduces event reconstruction, and in Section 5,
simulation of air showers and of the IceTop tank response are presented. In Section 6 the final
event selection and detector performance are discussed. Section 7 describes the determination of
the primary energy, whereas systematic uncertainties are discussed in Section 8. In Section 9 the
results are presented and discussed.
∗Corresponding author
Email address: fabian.kislat@desy.de (F. Kislat)
1Physics Department, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA
2Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3also Sezione INFN, Dipartimento di Fisica, I-70126, Bari, Italy
4NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
3

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−600 −400−2000 200 400600
X / m
−600
−400
−200
0
200
400
600
Y / m
2005
2006
2007
2008
2009
2010
2011
Figure 1: Layout of the IceTop air shower array. Colors indicate the year of deployment and the 26 stations installed
in 2007 are highlighted.
2. The detector
2.1. IceTop
The IceTop air shower array is the surface component of IceCube, covering an area of about
1km2with 81 detector stations above the 86 IceCube strings. The stations are mostly located next
to IceCube strings with a average spacing of 125m, except for three stations placed as an infill
with a smaller spacing in the central part of the detector, in order to lower the energy threshold
of the detector to about 100TeV. By 2007, 22 IceCube strings and 26 IceTop stations had been
deployed. These stations are highlighted in Fig. 1, which shows the layout of the IceTop air shower
array in its final configuration.
Each station consists of two ice-filled tanks separated from each other by 10m. The two tanks of
each station are embedded in snow with their tops aligned with the surface in order to minimize the
accumulation of drifting snow (see Section 2.5) and to protect the ice from temperature variations.
The tanks are cylindrical with an inner diameter of 1.82m, and are filled with transparent ice to
a depth of 90cm (see Fig. 2). The inner tank walls are covered with a diffusely reflective zirconium
coating. The first four stations deployed in 2005 and four tanks of the infill have a Tyvek liner with
a higher reflectivity. This difference affects amplitude and pulse width of detected tank signals,
since the higher reflectivity reduces Cherenkov photon absorption, leading to longer pulses.
Each tank is equipped with two ‘Digital Optical Modules’ (DOMs) [4] to record Cherenkov light
generated by charged particles passing through the tank. The DOMs are identical to those used
in other IceCube components and consist of a 10??photomultiplier tube (PMT) [5], plus electronic
circuitry for signal digitization, readout, triggering, calibration, data transfer and various control
4

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Perlite
Ice
DOMs
Wooden lid
40cm
58cm
Insulation
Diffusely reflective liner
(Tyvek / Zirconium)
90cm
91cm
Figure 2: Cross section of a tank showing the tank geometry with insulation and position of the DOMs. The center
of the ice surface between the two DOMs is used as tank position by reconstruction algorithms.
functions. The two DOMs in each tank were operated at different PMT gains, 5 · 106(high-gain
DOM) and 5 · 105(low-gain DOM), to enhance the dynamic range. This resulted in a linear
dynamic range from 1 to more than 105photoelectrons (PE). During the data taking period used
in this analysis all 104 DOMs in the 26 IceTop stations were fully operational.
2.2. Trigger and data acquisition
A DOM records PMT signals autonomously. A signal is recorded if it surpasses a certain
discriminator threshold, which in the case of IceTop was set to 22mV for the high-gain DOMs
(corresponding to about 20pe) and 12mV for the low-gain DOMs (corresponding to about 180pe).
The exact charge threshold depends on the pulse shape, which is determined by the arrival times of
photoelectrons. After triggering, the delayed PMT pulse is sampled by ‘Analog Transient Waveform
Digitizers’ (ATWDs) with three different gain channels (nominal gains are 0.25, 2, and 16) in 128
bins with a width of 3.3ns, corresponding to a total sampling time of about 422ns. The analog
samples are then digitized to 10 bits accuracy.
Up to this point, signal recording happens independently in each DOM. To reduce the high
trigger rates in high-gain DOMs (∼2kHz), which are mostly from low-energy showers, a hardware
‘local coincidence’ between the high-gain DOMs in the two tanks of a station is required to initiate
the readout and transmission of DOM data to the counting house (IceCube Lab). The digitizing
process is aborted if the high-gain DOM in the neighboring tank does not also measure a signal
above threshold within a time window of ±1µs. The IceTop trigger condition is satisfied, if six or
more DOMs report a (local coincident) signal within a time window of 5µs, which initiates readout
of all DOMs from 10µs before the first until 10µs after the last of the six DOM triggers which
5

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Time / ns
050 100 150 200250 300350 400
pe / 3.3ns
DOM 47-61: Charge 1.18 VEM
10
8
6
4
2
0
Figure 3: Left: A typical IceTop waveform. The blue horizontal line marks the baseline and the near vertical green
line indicates the extrapolation of the leading edge yielding the signal time marked by the red circle. The baseline
is below 0 (dashed line) due to droop. Right: A typical charge spectrum recoded for the VEM calibration. The
spectra are fitted with an empirical formula to determine the peak position (see text).
initiated the readout. The requirement of 6 DOMs means that at least two stations had to trigger.
In 2007, the total IceTop trigger rate was about 14Hz.
2.3. Charge extraction and calibration
Figure 3 shows a typical waveform measured in IceTop. While waveforms are recorded in
three ATWD channels, this analysis used only the highest gain unsaturated (less than 1022 ADC
counts) channel. In this analysis only the integrated charge and the signal time were used. Before
a waveform was integrated, its baseline was subtracted by determining the average value in bins
83 to 123 highlighted in the figure. The undershoot is caused by droop introduced by the ferrite-
core transformer used to couple the photomultiplier tube to the DOM’s front-end electronics. The
signal time (‘leading edge time’) was defined by extrapolating the steepest rise of the waveform
before the maximum down to the baseline. The absolute time scale of a DOM is calibrated with
respect to all other DOMs to an accuracy of about 2ns RMS [6].
The charge produced by a single photoelectron, the amplifier gains and the digitizers are cali-
brated in a procedure common to all IceCube DOMs [6]. However, the signal response to a particle
of a given type and energy traversing the tank, expressed in photoelectrons, differs from tank to
tank, due to differences in ice quality and reflectivity of the tank walls. Therefore, the signal of
each tank is converted to a common unit called ‘Vertical Equivalent Muon’ (VEM). Calibration
was done by recording charge spectra of DOMs in dedicated calibration runs with all DOMs op-
erated at a gain of 5 · 106and without requiring local coincidence (for an example see Fig. 3,
right). These charge spectra show a clear peak due to penetrating muons above a background of
electrons and photons. The spectra are fitted by the sum of a function describing the muon peak
and an exponentially falling background term. Measurements with a portable scintillator telescope
6

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mounted on top of tanks, restricting muons to nearly vertical angles of incidence, indicated that
the muon peak lies about 5% lower than for the full angular range. Simulation studies confirmed
that restricting the angles of incidence of muons shifts the peak position by about 5% [7]. The
scaled peak is referred to as ‘VEM peak’. For a given DOM the VEM unit can be expressed in
terms of number of photoelectrons. These values average 120 and 200 photoelectrons for the low
and high reflectivity tanks (see above), respectively.
For the 5-month run, 15 calibration runs were used. Between two consecutive calibration runs,
the charge calibration was assumed to be stable (see also the discussion in Section 8.4).
2.4. Atmospheric conditions
Variations of the atmosphere influence the development of air showers and thus the signals
measured in IceTop. Since IceTop is below the shower maximum for all energies of interest in
this analysis and for all primary masses, an increase of the atmospheric overburden leads to an
attenuation of shower sizes. Atmospheric overburden is related to ground pressure p as X0= p/g,
where g = 9.87m/s2is the gravitational acceleration at the South Pole. While there is some annual
variation of the ground pressure, it mostly varies on shorter time scales on the order of days.
Besides ground pressure, the altitude profile of the atmosphere, dXv(h)/dh, also influences the
development of air showers. This altitude profile has a pronounced annual cycle because the cold
atmosphere during the winter months is much denser than the warmer atmosphere of the summer
months. The data used in this analysis were mostly taken during the winter months.
In the simulations used to interpret the air shower data a model of the South Pole atmosphere is
used, which should represent the average atmosphere during the data taking period. Nevertheless,
variations of the atmosphere around the average lead to an additional uncertainty on the measured
energy spectrum. These systematic uncertainties will be discussed in Section 8.2.
2.5. Snow
During installation, IceTop tanks are embedded in snow up to the upper surface of the tanks.
Depending on location, surrounding surface and structures, each tank is covered by accumulated
layers of snow of varying thickness. Each year the amount of snow on the IceTop tanks grows by
an average of 20cm.
As shown in Fig. 4, the snow height for the analyzed data varied mostly between 0 and 30cm,
except for four stations close to a building, which are covered by 60 to 90cm of snow. The average
snow height was 20.5cm in January, 2007.
The snow has an average density of 0.38g/cm3, depending on snow height and location. The
snow on top of and around the tanks influences the response to air shower particles penetrating the
tanks and needs to be taken into account in simulations and for the determination of the shower
energy.
7

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Snow depth / m
0 0.20.40.60.81 1.2 1.41.6 1.8
# Tanks
0
2
4
6
8
10
12
14
16
18
20
22
IceTop-26 tanks
Snow in 2007 (Av. 20.5cm)
Snow in 2008 (Av. 53.2cm)
Figure 4: Snow heights on top of IceTop tanks measured in January 2007. All 20 newly deployed tanks had no snow
on top, the average snow height was 20.5cm. The dashed histogram is the snow height distribution on top of the
same tanks measured one year later.
3. Data set and data selection
Event filtering and data transmission. The data used in this analysis were taken between June 1st
and October 31st, 2007. The analysis was performed using a data sample which was transferred
via satellite to the IceCube data center at UW Madison with limited bandwith. Due to these
bandwidth constraints, events with less than 16 participating DOMs were prescaled by a factor
of 5. Events with 16 or more DOMs were transmitted at a rate of 0.9Hz and the small events at
a rate of 2.5Hz.
Run selection. In order to ensure detector stability and data quality, the following criteria were
applied to runs which were used in this analysis:
• The run was longer than 30min. A normal detector run lasted 8 hours, and nearly all runs
that were aborted after a short time encountered some sort of problem.
• All DOMs were running stably.
• After correction for atmospheric pressure variations the trigger and filter rates were stable
and within ±5% agreement with the previous good run. Pressure correction was done by
fitting the relation between ground pressure p and rate R with an exponential function,
R(p) ∼ exp(−β p), yielding a barometric coefficient β = 0.0077/mbar [8]. Then, the rates
were corrected to the average South Pole ground pressure of 680mbar:
Rcorrected= R exp?β (p − 680mbar)?.
(1)
These cuts reduced the livetime by about 10%.
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Event cleaning. Before starting the reconstruction, events were cleaned based on a few simple
timing criteria. In case both DOMs of a tank triggered, the tank signal was rejected if the time
difference between the two signals was greater than 40ns. The analysis used only one signal per
tank. For each high-gain DOM a saturation threshold was determined from a comparison of signals
that triggered both DOMs in a tank. Signals with less charge were taken from the high-gain DOM.
If the charge exceeded the saturation threshold, the charge measured by the low-gain DOM was
used and the time was determined from the high-gain signal. Furthermore, a tank signal was also
rejected if only the low-gain DOM triggered and the high-gain DOM was missing.
Then, a maximum time difference of
|tA− tB| <|xA− xB|
c
+ 200ns
(2)
between signals in tanks A and B of the same station was required. Here, tA and tB are the
signal times in the two tanks and xAand xBare the tank locations. The tolerance of 200ns was
introduced in order to account for shower fluctuations. Finally, stations were grouped in clusters,
such that any pair of stations i and j in the cluster fulfilled the condition
|ti− tj| <|xi− xj|
c
+ 200ns.
(3)
The station position xiis the center of the line connecting its two tanks, and tiis the average time
of the tank signals. In each event, only the largest cluster of stations was kept.
Only about 10% of events were affected by this event cleaning, and about 2.5% of events
dropped below the threshold of 5 stations required for reconstruction.
Charge-based retriggering. In order to reduce uncertainties due to the description of the detector
threshold in the simulation, all events were retriggered to a common threshold based on total
registered charge. All pulses with a charge below Sthr= 0.3VEM were removed, and afterwards
the local coincidence conditions (see Section 2.2) were re-evaluated discarding all pulses that no
longer fulfilled this condition. This procedure was applied to both experimental and simulated
data.
Event selection. For further processing, a total of Ntot= 8895205 events were selected where at
least five stations had triggered. Events which fulfilled this condition, but had less than 16 DOMs
read out (before event cleaning), were reweighted in the analysis with the prescale factor of 5 (see
above).
The effective livetime was calculated by fitting the distribution of time differences between
events, ∆t, with an exponential function,
N(∆t) = N0exp(−∆t/τ).
(4)
This was done individually for each data taking run. The selected runs have a total effective
livetime of T =?
days period. The uncertainty on the livetime was included in the statistical error.
runs i(Ni·τi) = (3274.0±1.9)h, which corresponds to 89.4% of the selected 153
9

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4. Air shower reconstruction
The energy of the primary particle cannot be measured directly, but has to be determined from
the air shower parameters. Properties of an air shower that are reconstructed by IceTop are the
shower core position, its direction, and the shower size. The latter is a measure of primary energy
and is defined as the signal Sref measured at a certain distance Rref from the shower axis. These
properties are reconstructed by fitting the measured charges with a lateral distribution function
and the signal times with a function describing the geometric shape of the shower front.
4.1. The reference radius Rref
The average logarithmic distance to the shower axis, ?logR?, of signals participating in the fit
for the given array configuration and energy range under investigation is about 125m. While this
number does depend on the primary energy and mass, it is limited by the relatively small size and
the particular geometry of the 26-station array. A constant Rref= 125m was chosen in order to
minimize the correlation between the parameters Srefand β in the fit. The shower size parameter
is thus referred to as S125.
4.2. Time and charge distribution of air shower signals
Lateral charge distribution. IceTop tanks are not only sensitive to the number of charged particles,
but also detect photons. Furthermore, the signal generated by a particle when it traverses the tank
also depends on incident particle type, energy and direction. Therefore, the charge expectation
value in an IceTop tank at distance R from the shower axis was described by an empirical lateral
distribution function found in Monte Carlo simulations [9]:
S(R) = Sref·
?
R
Rref
?−β−κ log(R/Rref)
.
(5)
This is a second order polynomial in logR for the logarithm of the signal, logS(R):
log S(R) = log Sref− β log
?
R
Rref
?
− κ log2
?
R
Rref
?
.
(6)
This function behaves unphysically at small distances to the shower axis (R ? 1m). However, as
described in the next subsection, all signals within 11m of the core, are excluded from the fit. The
free parameters of the function, in addition to the shower size, Sref, are β and κ, corresponding to
the slope and curvature in the logarithmic representation at R = Rref. The parameter κ is fixed
at the average value of 0.303 found in simulation studies and it was verified that this constraint
does not have a significant impact on the result. Therefore, a fit of function (6) depends only
on two explicit parameters (Sref, β) and, since R depends on shower core position (xc, yc) and
direction (θ,φ), implicitly on four more.
In the following we will only refer to the reference radius of 125m motivated in the previous
subsection. Figure 5 shows an example of the lateral distribution function fit of a shower with 25
triggered stations.
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R / m
2
10
3
10
S / VEM
-1
10
1
10
2
10
3
10
High Gain DOMs
Low Gain DOMs
2.8) VEM
±
= (65.1
125
S
0.07
±
= 2.66
β
→ upstream R / m downstream ←
-500 -400 -300 -200 -100
-300
0 100 200 300400 500
t / ns
∆
-250
-200
-150
-100
-50
0
High Gain DOMs
Low Gain DOMs
Figure 5: Left: Example of an IceTop lateral fit. The shower triggered 25 stations and the reconstructed shower size
is S125 = (65.1 ± 2.8)VEM. Right: Time residuals with respect to a plane perpendicular to the shower direction
given by Eq. (8). “Upstream” and “downstream” refer to tanks being hit before and after the shower core reaches
the ground.
Time distribution. The arrival times of the signals map out the shower front. The expected signal
time of a tank at the position x was thus parametrized as
t(x) = t0+1
c(xc− x) · n + ∆t(R).
(7)
Here, t0is the time the shower core reaches the ground, xcis the position of the shower core on
the ground and n is the unit vector in the direction of movement of the shower. The ground was
√S-weighted average of participating tank altitudes, which varied by about 3m.
defined as the
The term ∆t(R) describes the shape of the shower front as a function of distance R to shower
axis and is the time residual with respect to a plane perpendicular to the shower axis which
contains xc. Experimentally, the shower front can be described by the sum of a parabola and a
Gaussian function, both symmetric around the shower axis:
∆t(R) = aR2+ b
?
exp
?
−R2
2σ2
?
− 1
?
,
(8)
with the constants
a = 4.82310−4ns/m2,b = −19.41ns,σ = 83.5m.
Function (7) is fitted to the measured signal times with five free parameters: two for the core
position, two for the shower direction and one for the reference time t0. Hence, the complete air
shower reconstruction has the following parameters: position of the shower core (xc,yc), shower
direction θ and φ, shower size S125, slope parameter β, and time at ground t0.
4.3. Likelihood fit
Likelihood function. The functions (6), (7) and (8) describing the expectations for the charge and
time of air shower signals were fitted to the measured data using the maximum likelihood method.
In addition to terms for the signal charges and times, the likelihood function also takes into account
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Page 12

stations that did not trigger so that the full likelihood function consisted of three factors. As usual
we use the logarithm of the likelihood function:
L = Lq+ L0+ Lt.
(9)
The first term,
Lq= −
?
i
?logSi− logSfit
i
?2
2σ2
q(Sfit
i)
−
?
i
ln?σq(Sfit
i)?,
(10)
describes the probability of measuring the charges Siif the fit expectation value at the position of
the tank is Sfit
i
as given by the lateral distribution function (5). The sum runs over all tanks that
have triggered. The signal fluctuations are described by a normal distribution of logSi around
logSfit
i, with standard deviations σqdepending on the signal charge. The charge dependence of σq
has been determined experimentally from the local shower fluctuations between the two tanks of
a station and are reasonably well reproduced by simulation [10]. It can roughly be described by
a linear improvement of log(σq(logS)) until a saturation level is reached at S ≈ 120VEM. The
second sum in Lq accounts for the proper normalization of the signal likelihood and is required
because the standard deviations σqdepend on the fitted signals.
The next term of the log-likelihood function (9),
L0=
?
j
ln
?
1 −?Phit
j
?2?
,
(11)
accounts for all stations j that did not trigger. The probability that one tank in station j delivers
a signal at a given charge expectation value is
Phit
j
=
1
√2πσq(Sfit
j)·
∞
?
log Sthr
j
exp
?
−
?logSj− logSfit
2σ2
j
?2
q(Sfit
j)
?
dlogSj.
(12)
The lower integration limit is defined through the charge threshold of Sthr
j
= 0.3VEM for the tank
signal, as determined by the retriggering procedure described in Section 3. The charge expectation
value, Sfit
j, was evaluated for the center of a line joining the centres of the two tanks. Since
the two tanks of one station are operated in coincidence, there are no single untriggered tanks.
Equation (11) is an approximation because it assumes that Phit
j
in the two tanks is independent. Of
course, there is a natural correlation in the signal expectation values of two nearby tanks because
they have a similar value of the lateral distribution function. However, the fluctuations about this
expectation value are assumed to be uncorrelated.
The third term of function (9), Lt, describes the probability for the measured set of signal
times,
Lt= −
?
i
(ti− tfit
2σ2
t(Ri)
i)2
−
?
i
ln(σt(Ri)/ns),
(13)
where the index i runs over all tanks, tiis the measured signal time of tank i and tfit
i
= t(xi) is
the fitted expectation value according to function (7). The arrival time fluctuations σt(Ri) depend
on the distance Riof tank i to the shower axis, and are the RMS of the arrival time distribution
found in experimental data [10].
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Page 13

Fit procedure. The likelihood fit was seeded with first-guess calculations for the core and the
direction of the shower. As a first estimate of the core position the centre-of-gravity of tank
positions xiweighted with the square root of the charges was calculated:
xCOG=
?
i
√Sixi
?
i
√Si
.
(14)
The square root of S used as a weight was chosen based on a study of the achievable fit accuracy.
The starting values for shower direction and arrival time were obtained by fitting a plane to the
signal times.
The likelihood minimisation is then done in several iterations to improve the stability of the
fit. At first the shower direction is fixed and only the lateral fit of the charges is iterated with the
free parameters S125, β, and core position. After each iteration, those tanks that are closer than
11m to the shower axis are removed from the fit. Iteration is stopped when no more tanks are
removed from the fit. The reason for this step was that very large signals tended to unnaturally
attract shower cores, which had a negative effect on the shower core resolution in the vicinity of
stations. Additionally, this mitigated the effect of saturated pulses. Then, a final iteration is done
in which description of the shower curvature is included and the shower direction is varied.
5. Simulation of air showers and the IceTop detector
The relation between the measured signals and the energy of the primary particle, as well as
detection efficiency and energy resolution were obtained from CORSIKA [11] air shower simulations
and simulations of the IceTop detector.
5.1. Air shower simulation
We simulate the development of air showers in the atmosphere using the simulation code COR-
SIKA [11]. Inside CORSIKA, the hadronic component of the air showers was simulated using the
models SIBYLL2.1 [12, 13] and FLUKA 2008.3 [14, 15] for the high and low energy interactions,
respectively. The electromagnetic component was simulated using the EGS4 code [16] and no
‘thinning’ (reduction of the number of traced particles) was applied. To study systematic effects
of the hadronic interaction model, small samples of showers were simulated using the QGSJET-
II [17, 18] and EPOS 1.99 [19] high energy interaction model. Two different parameterizations of
the South Pole atmosphere from two days in 1997 based on the MSIS-90-E model [20] were used:
July 1st and October 1st (CORSIKA atmospheres 12 and 13). The July atmosphere has a total
overburden of 692.9g/cm2, while the October atmosphere has an overburden of 704.4g/cm2. The
July atmosphere was used in the data analysis, because its total overburden is close to the average
measured overburden of 695.5g/cm2and its profile corresponds to that of a South Pole winter
atmosphere. The October atmosphere model was used to study systematic uncertainties due to
the atmospheric profile used in the simulation.
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5.2. Detector simulation
The output of the CORSIKA program, i.e. the shower particle types, positions and momenta at
the observation level of 2835m, were injected into the IceTop detector simulation. The simulation
determines the amount of light produced by the shower particles in the tanks followed by the
simulation of the PMT, the DOM electronics and the trigger chain.
The Cherenkov emission inside the tanks is simulated using Geant4 [21, 22]. All structures of
the tank, the surrounding snow, including individual snow heights on top of each tank, as well
as the air above the snow are modeled realistically [23]. The snow heights used in the simulation
corresponded to those measured in January 2007 (see Fig. 4). In order to save computing time,
Cherenkov photons are not tracked; only the number of photons emitted in the wavelength interval
300nm to 650nm is recorded. Using Geant4 simulations, that include Cherenkov photon tracking
until photons reach the PMT, it was shown that the number of detected photons scales linearly
with the number of emitted photons, independent of incident particle type and energy.The
propagation of Cherenkov photons is modeled by distributing the arrival times according to an
exponential distribution, which is tuned such that simulated waveform decay times match those
observed in experimental data (26.5ns for zirconium lined tanks and 42.0ns for tanks with Tyvek
bag).
The number of photoelectrons corresponding to 1VEM was taken from the VEM calibration of
the real tanks and used as an input for the simulation. The simulated tanks were then calibrated
by generating muon spectra as in experimental data using air shower simulations with primary
energies between 3GeV and 30TeV and zenith angles up to 65◦. Thus, the ratio between the
number of emitted Cherenkov photons and observed photoelectrons was determined by the VEM
calibration of simulated tanks.
In the next step the generated photoelectrons are injected into a detailed simulation of the
PMT followed by the analog and digital electronics of the DOM. To simulate the photomultipliers,
Gaussian single photoelectron waveforms with a random charge according to the average single
photoelectron spectrum are superimposed [5]. Afterwards, a saturation function is applied to
the resulting waveforms. In the DOM simulation, the pulse shaping due to the analog front end
electronics is applied to the output of the PMT simulation. This includes the individual shaping of
the signal paths to the ATWD and the discriminators, as well as the simulation of the droop effect
induced by the toroid that couples the high voltage circuits of the PMT to the readout electronics.
Then, the discriminators are simulated and the local coincidence conditions are evaluated. Finally,
the waveform digitization and the array trigger are simulated.
Simulated data are of the same format as the experimental data and were reconstructed in the
same way, as described in the previous section.
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5.3. Simulation datasets
In this analysis we describe the cosmic ray composition just with the two extreme elements
hydrogen and iron. The justification comes from the fact that the final result is not sensitive to
details of the composition but only to the mean logarithmic mass.
In total 2 · 105showers of proton and iron primaries in the energy range between 100TeV
and 100PeV were generated in 30 logarithmic energy bins according to an E−1spectrum. For
the analysis, the events are reweighted to an E−3flux, which is closer to the results of previous
experiments and thus reduces systematic biases (see also Section 8.9). In addition to pure proton
and iron simulations we also combined the datasets using a parametrization of Glasstetter’s two-
component model [24]. We transformed the proton flux to the form
dI
dlnE= I0
?
E
1PeV
?γ1+1?
1 +
?
E
Eknee
?ε?(γ2−γ1)/ε
,
(15)
as suggested in [25], with I0= 3.89 · 10−6m−2s−1sr−1, γ1= −2.67, γ2= −3.39, Eknee= 4.1PeV,
and ε = 2.1. The iron flux was used as specified in Ref. [24]:
dI
dlnE= 1.95 · 10−6m−2s−1sr−1·
?
E
1PeV
?−1.69
.
(16)
The total flux was then normalized to the same E−3spectrum as in case of the single component
Monte Carlo.
Since shower generation is CPU intensive the same showers were sampled several times inside
a circle with a radius of 1200m around the center of the 26 station IceTop array. The number of
samples was chosen for different energy bins such that every shower would remain on average only
once in the final sample after applying the cuts described in the next section. This ensures a good
balance between an effective use of the generated showers and the artificial fluctuations introduced
by oversampling.
6. Event selection and reconstruction performance
Quality cuts. Based on the reconstruction results the following quality criteria were required for
each event entering the final event sample, for both simulated and experimental data:
• Containment cut: The reconstructed core and the first-guess core position had to be at least
50m inside the boundary of the array. The array boundary is defined by the polygon with
vertices at the centers of stations at the periphery of the array and edges connecting these
stations. This cut defines a fiducial area of Acut= 0.122km2. Furthermore, it was required
that the station containing the largest signal is not on the border of the array.
• Only events with zenith angles θ < 46◦were considered.
• The reconstruction uncertainty on the core position had to fulfill σcore=
?
σ2
x+ σ2
y< 20m.
15