PHYSICAL REVIEW D 83, 092003 (2011)

Constraints on the extremely-high energy cosmic neutrino flux with the IceCube 2008-2009 data
R. Abbasi,28 Y. Abdou,22 T. Abu-Zayyad,33 J. Adams,16 J. A. Aguilar,28 M. Ahlers,32 K. Andeen,28 J. Auffenberg,38
X. Bai,31 M. Baker,28 S. W. Barwick,24 R. Bay,7 J. L. Bazo Alba,39 K. Beattie,8 J. J. Beatty,18,19 S. Bechet,13 J. K. Becker,10
K.-H. Becker,38 M. L. Benabderrahmane,39 S. BenZvi,28 J. Berdermann,39 P. Berghaus,28 D. Berley,17 E. Bernardini,39
D. Bertrand,13 D. Z. Besson,26 D. Bindig,38 M. Bissok,1 E. Blaufuss,17 J. Blumenthal,1 D. J. Boersma,1 C. Bohm,34
D. Bose,14 S. Böser,11 O. Botner,37 J. Braun,28 A. M. Brown,16 S. Buitink,8 M. Carson,22 D. Chirkin,28 B. Christy,17
J. Clem,31 F. Clevermann,20 S. Cohen,25 C. Colnard,23 D. F. Cowen,36,35 M. V. D’Agostino,7 M. Danninger,34
J. Daughhetee,5 J. C. Davis,18 C. De Clercq,14 L. Demirörs,25 T. Denger,11 O. Depaepe,14 F. Descamps,22 P. Desiati,28G. de Vries-Uiterweerd,22 T. DeYoung,36 J. C. Dı́az-Vélez,28 M. Dierckxsens,13 J. Dreyer,10 J. P. Dumm,28 R. Ehrlich,17
J. Eisch,28 R. W. Ellsworth,17 O. Engdegård,37 S. Euler,1 P. A. Evenson,31 O. Fadiran,4 A. R. Fazely,6 A. Fedynitch,10
T. Feusels,22 K. Filimonov,7 C. Finley,34 T. Fischer-Wasels,38 M. M. Foerster,36 B. D. Fox,36 A. Franckowiak,11
R. Franke,39 T. K. Gaisser,31 J. Gallagher,27 M. Geisler,1 L. Gerhardt,8,7 L. Gladstone,28 T. Glüsenkamp,1 A. Goldschmidt,8J. A. Goodman,17 D. Gora,39 D. Grant,21 T. Griesel,29 A. Groß,16,23 S. Grullon,28 M. Gurtner,38 C. Ha,36 A. Hallgren,37
F. Halzen,28 K. Han,39 K. Hanson,13,28 D. Heinen,1 K. Helbing,38 P. Herquet,30 S. Hickford,16 G. C. Hill,28
K. D. Hoffman,17 A. Homeier,11 K. Hoshina,28 D. Hubert,14 W. Huelsnitz,17 J.-P. Hülß,1 P. O. Hulth,34 K. Hultqvist,34
S. Hussain,31 A. Ishihara,15,* J. Jacobsen,28 G. S. Japaridze,4 H. Johansson,34 J. M. Joseph,8 K.-H. Kampert,38 A. Kappes,9T. Karg,38 A. Karle,28 J. L. Kelley,28 P. Kenny,26 J. Kiryluk,8,7 F. Kislat,39 S. R. Klein,8,7 J.-H. Köhne,20 G. Kohnen,30
H. Kolanoski,9 L. Köpke,29 S. Kopper,38 D. J. Koskinen,36 M. Kowalski,11 T. Kowarik,29 M. Krasberg,28 T. Krings,1G. Kroll,29 T. Kuwabara,31 M. Labare,14 S. Lafebre,36 K. Laihem,1 H. Landsman,28 M. J. Larson,36 R. Lauer,39
J. Lünemann,29 J. Madsen,33 P. Majumdar,39 A. Marotta,13 R. Maruyama,28 K. Mase,15 H. S. Matis,8 K. Meagher,17
M. Merck,28 P. Mészáros,35,36 T. Meures,1 E. Middell,39 N. Milke,20 J. Miller,37 T. Montaruli,28,† R. Morse,28
S. M. Movit,35 R. Nahnhauer,39 J. W. Nam,24 U. Naumann,38 P. Nießen,31 D. R. Nygren,8 S. Odrowski,23 A. Olivas,17
M. Olivo,10 A. O’Murchadha,28 M. Ono,15 S. Panknin,11 L. Paul,1 C. Pérez de los Heros,37 J. Petrovic,13 A. Piegsa,29
D. Pieloth,20 R. Porrata,7 J. Posselt,38 P. B. Price,7 G. T. Przybylski,8 K. Rawlins,3 P. Redl,17 E. Resconi,23 W. Rhode,20
M. Ribordy,25 A. Rizzo,14 J. P. Rodrigues,28 P. Roth,17 F. Rothmaier,29 C. Rott,18 T. Ruhe,20 D. Rutledge,36
B. Ruzybayev,31 D. Ryckbosch,22 H.-G. Sander,29 M. Santander,28 S. Sarkar,32 K. Schatto,29 T. Schmidt,17
A. Schönwald,39 A. Schukraft,1 A. Schultes,38 O. Schulz,23 M. Schunck,1 D. Seckel,31 B. Semburg,38 S. H. Seo,34
Y. Sestayo,23 S. Seunarine,12 A. Silvestri,24 A. Slipak,36 G. M. Spiczak,33 C. Spiering,39 M. Stamatikos,18,‡ T. Stanev,31
G. Stephens,36 T. Stezelberger,8 R. G. Stokstad,8 A. Stössl,39 S. Stoyanov,31 E. A. Strahler,14 T. Straszheim,17 M. Stür,11
G. W. Sullivan,17 Q. Swillens,13 H. Taavola,37 I. Taboada,5 A. Tamburro,33 A. Tepe,5 S. Ter-Antonyan,6 S. Tilav,31
P. A. Toale,2 S. Toscano,28 D. Tosi,39 D. Turčan,17 N. van Eijndhoven,14 J. Vandenbroucke,7 A. Van Overloop,22
J. van Santen,28 M. Vehring,1 M. Voge,11 C. Walck,34 T. Waldenmaier,9 M. Wallraff,1 M. Walter,39 Ch. Weaver,28
C. Wendt,28 S. Westerhoff,28 N. Whitehorn,28 K. Wiebe,29 C. H. Wiebusch,1 D. R. Williams,2 R. Wischnewski,39
H. Wissing,17 M. Wolf,23 T. R. Wood,21 K. Woschnagg,7 C. Xu,31 X. W. Xu,6 G. Yodh,24 S. Yoshida,15 and P. Zarzhitsky2(IceCube Collaboration)
1

III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
3
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, Alaska 99508, USA
4
CTSPS, USAClark-Atlanta University, Atlanta, Georgia 30314, USA
5
School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
6
Department of Physics, Southern University, Baton Rouge, Louisiana 70813, USA
7
Department of Physics, University of California, Berkeley, California 94720, USA
8
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
9
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
10
Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
11
Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany
12
Department of Physics, University of the West Indies, Cave Hill Campus, Bridgetown BB11000, Barbados
13
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
14
Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
15Department of Physics, Chiba University, Chiba 263-8522, Japan
16
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand21550-7998= 2011=83(9)=092003(9)092003-1

Ó 2011 American Physical Society

R. ABBASI et al.

PHYSICAL REVIEW D 83, 092003 (2011)17

18

Department of Physics, University of Maryland, College Park, Maryland 20742, USA
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210, USA
19
Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA
20
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germany
21
Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
22Department of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
23
Max-Planck-Institut für Kernphysik, D-69177 Heidelberg, Germany
24
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
25
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland
26
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
27
Department of Astronomy, University of Wisconsin, Madison, Wisconsin 53706, USA
28
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
29
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
30
Université de Mons, 7000 Mons, Belgium
31
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
32
Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
33
Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA
34
Oskar Klein center and Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
35
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
36
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA37
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
38
Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
39
DESY, D-15735 Zeuthen, Germany(Received 22 March 2011; published 24 May 2011)
We report on a search for extremely-high energy neutrinos with energies greater than 106 GeV using
the data taken with the IceCube detector at the South Pole. The data was collected between April 2008 and
May 2009 with the half-completed IceCube array. The absence of signal candidate events in the sample of
333.5 days of live time significantly improves model-independent limits from previous searches andallows to place a limit on the diffuse flux of cosmic neutrinos with an E2 spectrum in the energy range
2:0  106  6:3  109 GeV to a level of E2   3:6  108 GeV cm2 sec1 sr1 .
DOI: 10.1103/PhysRevD.83.092003

PACS numbers: 98.70.Sa, 95.55.Vj

I. INTRODUCTION
Cosmogenic neutrinos, the daughter particles of theGreisen-Zatsepin-Kuzmin (GZK) process in which thehighest energy cosmic rays interacting with the cosmicmicrowave background [1,2], may give a unique picture of
the Universe in the highest energy regime. Cosmogenic
neutrinos carry information about the sources of the highest energy cosmic rays, such as their location, cosmological evolution, and cosmic-ray spectra at the sources.
Various cosmogenic neutrino models [3–6] which assume
primary cosmic ray protons predict neutrino fluxes E2  
104 GeV2 sec1 sr1 in the energy range 108 GeV 
E  1010 GeV, which implies that the 4 solid angle
averaged neutrino effective area divided by energyA =E must be larger than 105 m2 =GeV (e.g. A 
103 m2 at 108 GeV and A  104 m2 at 109 GeV) todetect several cosmogenic neutrinos every year.
*Corresponding author: aya@hepburn.s.chiba-u.ac.jp (A.
Ishihara)†
also Università di Bari and Sezione INFN, Dipartimento di
Fisica, I-70126, Bari, Italy‡
NASA Goddard Space Flight Center, Greenbelt, MD 20771,
USA

Several techniques have been used to realize such huge
detection volumes for these extremely-high energy (EHE)
neutrinos. Air-shower detectors search for neutrinoinduced young inclined showers [7] or Earth-skimming
events initiated by tau neutrinos [8]. Radio Cherenkov
neutrino detectors search for radio Askar’yan pulses in adielectric medium as the EHE neutrino signature [9–11].
Underground neutrino telescopes, such as IceCube, deployed in transparent naturally occurring media [12,13]
can detect EHE neutrino interactions through the strong
Cherenkov radiation emitted by the charged secondary
particles. This technique is well established for observations of astrophysical neutrinos in the MeV to GeV energy
region [14,15], and can also be utilized to search for cosmogenic EHE neutrinos with an appropriate backgroundrejection method. In a neutrino telescope, an EHE neutrino
interaction would be identified by the extremely-high number of Cherenkov photons deposited in the detector.
In this paper, we describe the search for neutrinos withenergies above 106 GeV using data collected with the halfcompleted IceCube detector in 2008-2009. This analysis issensitive to all three neutrino flavors. Compared to theprevious EHE neutrino search described in Ref. [13],which used an earlier stage of the IceCube detector, the092003-2

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PHYSICAL REVIEW D 83, 092003 (2011)

current analysis benefits from the enlarged instrumented
volume and from improved agreement between simulated
and observed event distributions. This article presents the
improved strategies implemented since the previous
analysis [13].

to the much higher light deposition. The total number ofphotoelectrons (NPE) recorded in an event was used as
the main distinctive feature to separate signal frombackground.
A. On-line sample

II. DATA SETS
The analysis uses data collected from April 6, 2008
through May 20, 2009. At the time of data collection, the
IceCube detector consisted of 2400 digital optical modules(DOMs) on 40 vertical strings. The volume of the detector
was roughly 0:5 Km3 with the detector center located at a
depth of 1948 m below the ice surface. The DOMs consistof a 25 cm photomultiplier tube [16] with data acquisitionand calibration electronics, data compression, communications, and control hardware [17]. The trigger setting was
unchanged from the previous analysis [13].
The analysis was optimized on simulated data with mostof the experimental data kept blind. A 10% subset of theexperimental data was used for examinations of theMonte Carlo simulations and detector response. This subset comprised 35.8 days of detector live time distributed
randomly throughout the data collection period, and was
not used once the analysis was fully defined. The use of astatistically independent final sample conservatively ensures avoidance of possible analysis bias due to tuning aMonte Carlo simulation using an experimental subset. The
selection criteria were then applied to the complementary
90% of the experimental data, comprising 333.5 days oflive time.
The primary background in this analysis is muon bundles
made up of large numbers of muons produced by highenergy cosmic-ray interactions in the atmosphere. Thisbackground was simulated with the CORSIKA air-shower
simulation package version 6.720 [18] with the SIBYLL 2.1[19] and QGSJET-II [20] hadronic interaction models, without prompt muons from the heavy meson decays. Cosmicray interactions assuming pure proton and iron primary
compositions in the energy region between 106 and1010 GeV were simulated. Background contributions
from primary cosmic-ray energies beyond 1010 GeV were
estimated by extrapolation of the simulated sample up to
the GZK cutoff energy of 5  1010 GeV. EHE neutrinosignal events in energies between 105 and 1011 GeV fromseveral flux models [3–6,21,22] were simulated using the
JULIET package [23].
III. EVENT SELECTION
The amount of energy deposited in the form of
Cherenkov photons by the neutrino-induced charged
particles in the detector is highly correlated with the energyof the particles [13]. An EHE neutrino interaction occurring inside or close to the IceCube detector would stand out
against the background of cosmic-ray induced muons due

The number of photoelectrons (p.e.) recorded by anindividual DOM was derived by integrating the pedestal
subtracted waveforms. Each DOM has two waveform digitizers, that simultaneously capture p.e. signals with differing dynamic ranges and time windows [17]. The event total
NPE was then obtained by summing the number of p.e.
detected by each DOM. photomultiplier tube saturation
effects and the sizes of the time windows limit the NPE
estimation at high light levels. The initial NPE calculation
was performed online at the South Pole. For this analysis
we consider only events with NPEonline  630. The event
rate of this ‘‘online bright sample’’ was 1:4 Hz. At thislevel, the background rate exceeded the expected signal
rate by  Oð107 Þ.
B. Off-line sample
For the following data selection step, the NPE values
were recalculated after eliminating photon signals from low
energy muons accidentally coincident in a 20 s time
window of a large NPE event. These low energy muons
leave a faint light, typically with an NPE < 9. The light
deposition of the coinciding low energy muon was, in mostcases, spatially and temporally separated from the mainbright p.e. cluster. While the few coincident photons havevery a small impact on the NPE calculation, they candisturb the geometrical reconstruction of the particle tracks
later on in the analysis. Contributions from coincident low
energy muons were eliminated by removing p.e. signalsthat were temporally separated from the time of the highest
light deposition associated with the main high NPE event.
The recording time of a p.e. signal in the ith DOM, t10;i , wasdefined as the time at which 10% of the total charge had
been captured. The time of the highest light deposition was
defined as the time tLN of the DOM which captured thelargest p.e. signal in the event. This time, tLN , was typicallyassociated with the time of closest approach of the charged
particle tracks to any DOM in the detector. For the offline
NPE calculation and track reconstruction, those p.e. signals
which occurred outside the time window [  4:4 s,
6:4 s] around the tLN were excluded. The ‘‘offline brightsample’’ selects events with NPE  3:2  103 and thenumber of hit DOMs ðNDOMÞ  200; here and below
NPE and NDOM are obtained after the tLN time windowcleaning. These NPE and NDOM thresholds reduced thebackground rate by 2 orders of magnitude while keeping
70% of the cosmogenic neutrino-induced events. The
remaining backgrounds are bundles containing many hundreds of muons, with an estimated cosmic-ray energy above
107 GeV.

092003-3

R. ABBASI et al.

PHYSICAL REVIEW D 83, 092003 (2011)

C. Quality cut
Apart from NPE, the particle direction and the depth
distribution of the detected Cherenkov photons are distinctive event features that separate the EHE neutrino signal
from the atmospheric muon background. Because of theenergy dependence of the neutrino interaction cross section, most of the EHE neutrino signal is expected fromdirections close to the horizon. As a result of the depth
dependence of the optical properties of the Polar ice, thelargest photon signals are often detected in the deepest partof the detector, where the ice is most transparent [24]. On
the other hand, the background atmospheric muons enter
the detection volume from above and lose a substantial
fraction of their energy during propagation through thedetector. Therefore, the time and depth coordinates, z, ofthe detected Cherenkov photons, measured relative to thedetector center, show negative correlation for background.
The largest photon signals from these background muons
are expected at shallow depths near the top of the detector.
Exceptions are inclined atmospheric muon bundles thatpass outside the instrumented volume with the point ofclosest approach in the deep, clear ice at the bottom of thedetector, or individual muons that deposit most of theirenergy in an isolated catastrophic energy loss in the deep
ice after having passed through the top part of the detector.
Track reconstructions often fail to identify such atmospheric muon events as downward-going tracks, whenmost of the light deposition occurs in the deep part of thedetector. Therefore, a track reconstruction is applied only
to those events in which the DOM with the largest signal islocated at z > 300 m (‘‘shallow events’’). The negative z
value indicates the vertical distance below the center of the
IceCube detector. For events with the largest photon
signal at z < 300 m (‘‘deep events’’), further event
selection criteria rely on timing instead of directional
information.
For the shallow events, the particle directions are reconstructed with the LineFit algorithm [13]. Since the majority

103

Number of Events

Number of Events

104
2

10
10
1
-1

10

10-2
10-3
-4

10

3.5

4

4.5 5 5.5 6log (NPE)
10

6.5

103

(b)
10
5

7

105

(c)

10

104
103
102
10
1
10-1
10-2
10-3
10-4
-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

10
1
10-1
10-2
10-3

cos (zenith angle)

3

10

(d)

102
10
1
-1

10

10-2
10-3

-4

10

experimental
background MC (Fe)background MC (H)signal MC (Model 1)

104

2

Number of Events(a)

Number of Events

105of the EHE neutrino-induced events is close to the horizon[23] while the directions of the background muon bundles
are mostly vertical, it is important to minimize the numberof background tracks that are misreconstructed as horizontal. In order to reject the misreconstructed background
events, another simple one-dimensional reconstruction is
introduced. The distribution of average depth of p.e. as afunction of timing is fitted by a linear function, zðt10 Þ ¼
C0 þ Szt  t10 . The fit parameter, Szt , is a measure for the
speed at which the light signal propagates in z-direction,and hence for the inclination of the tracks. For verticallydownward-going relativistic particles, the quantity Szt =ctakes values   1, where c is the vacuum speed of light,
whereas close to horizontal tracks yield values Szt =c  0.
The shallow ‘‘quality bright sample’’ requires an additional
condition of ðSzt =c þ cosÞ  0:4 where  is the reconstructed zenith angle from the LineFit. This condition
excludes events for which the one-dimensional fit suggests
a significantly more vertical downward-going geometry
than the LineFit. Both signal and background are reducedby less than 2% by this criterion. Figure 1 shows the
distributions of NPE (panel (a)) and cos (panel (b)) for
experimental data, background and signal simulations in
the quality bright sample. The distributions of CORSIKASIBYLL with an iron primary composition show a reasonable agreement with experimental data while the total
event rates are 50% overestimated by simulation. The
zenith angle reconstruction resolution of the shallow quality bright sample is 1:4 root mean square for muon
bundle background and  2:5 for  signal. This isbecause the  signal experiences more stochastic energy
losses along with hadronic cascades at its interaction
vertices.
The deep bright events (ZLN  300 m) are mostly
events that traverse the bottom edge of IceCube or are
uncontained events that propagate or cascade below thedetector. The inclination of these events tends to be reconstructed more horizontally than the true direction. The

4

4.5

5 5.5 6log10 NPE

6.5

7

10-4

0

1000

2000

3000

4000

∆ t LN-E [nsec]

FIG. 1. Event observables in the quality bright sample that are used for the final selection criteria. Distributions of (a) NPE and(b) cosine of the reconstructed zenith angle for shallow events, and (c) NPE and (d) tLNE for deep events in a live time of 333.5 days.
The black circles represent experimental data and the solid and dashed lines are CORSIKA-SIBYLL with iron and proton primaries,
respectively. The expected signal distributions from simulations of the GZK 1 model (sum of all three neutrino flavors) are shown as
long-dashed histograms. Systematic uncertainties are not included.

092003-4

CONSTRAINTS ON THE EXTREMELY-HIGH ENERGY . . .
104
103

103

2

2

10

0.5

10
1
0

10-1
10-2

-0.5

104

1

10-3

cos (zenith angle)cos (zenith angle)

1

10

0.5

10
1
0

10-1
10-2

-0.5

10-3

10-4

4

5
6
log10 NPE

7

4000

-1

102

4000

∆ tLN-E[nsec]

10
1
10-1

2000

10-4

10-5

10-2

4

5
6
log10 NPE

7

10
1
10-1

2000

10-2

10-3

10-3

-4

10-4

10
0

4

-5

5
6
log10 NPE

7

10-5

102

∆ tLN-E[nsec]

-1

10

0

4

5
6
log NPE

7

10-5

10

FIG. 2 (color online). Event number distributions of the shallow (upper panels) and deep (lower panels) quality bright sample
in 333.5 days are shown for the background (left panels) andsignal (right panels) simulations. The signal distributions arefrom GZK 1 model [3] adding all three flavors of neutrinos. The
background distributions are from CORSIKA-SIBYLL with ironprimaries. The series of thick lines in each panel indicate thefinal sample selection criteria.

agreement between the simulation and experimental distributions improves with increasing NPE threshold values
for these events. Events with NPE  104 are discarded
from the deep quality bright sample in order to achieve areasonable agreement between experimental data andsimulations. Since the majority of the EHE neutrinoinduced events have NPE  104 , the effect on the signal
efficiency by this requirement is minimal. A fraction of
96% of background is rejected by the cut, while 91% of thesignal is retained. Panel (c) in Fig. 1 shows the NPE
distributions from the deep quality bright sample.
D. Final selection
The final event selection is chosen in order to minimize
the model discovery factor (MDF ¼ lds =Nsignal ) [25] in

PHYSICAL REVIEW D 83, 092003 (2011)

the region of the phase space where a better signal tobackground ratio (S/B) is expected, where lds is the least
number of events to claim signal discovery at 5 significance and Nsignal is the number of neutrinos expected fromthe GZK 1 [3] model flux. For the shallow events, high S/B
is obtained in the region near the horizontal reconstructed
direction as shown in Fig. 1(b). For the deep events, insteadof reconstructing the inclination of events, we utilize thetime interval, tLNE , between the earliest detected photon
in an event and tLN to obtain the best S/B subsample. The
vertical atmospheric muon bundle events with the largest
number of p.e. near the bottom of IceCube are often associated with a small number of p.e. in the shallow detector
region much earlier than tLN . This contrasts to the EHE
neutrino signal events. The main contributions to a detectable EHE signal in IceCube come from neutrino-induced
horizontal muons and taus [23]. These produce the largest
number of p.e. signals shortly after the first recorded photoelectrons. Contained cascadelike events induced by neutrino interactions [26] inside the IceCube detector volume
also exhibit a similar trend. Figure 1(d) shows the distributions in the deep quality bright sample. The best S/B isachieved in the bin tLNE  0 ns. The high rate in theexperimental data for tLNE  3600 is due to random
noise in the DOMs and remaining coincident muons thatwere underestimated by the simulations. The slightly
higher rate for the data in the bin tLNE  0 ns may
reflect the fact that the ice is cleaner than what was simulated in the deep region. Figure 2 presents the event distributions in the planes of cos vs NPE for the shallow
events and tLNE vs NPE for the deep events.
Optimization is performed by differentiating the NPE
threshold numbers in the region cos  0:3 or tLNE 
0:5 s for the shallow and deep quality bright sample,
respectively. The NPE threshold of the other region( cos  0:3 or tLNE  0:5 s) is conservatively determined such that the number of background events above thethreshold is less than 104 of the full live time for each binof cos with width 0.2 or 1 s for tLNE . This improves
the detection sensitivity without sacrificing discovery potential. The solid lines in Fig. 2 are the final level selection
criteria determined from the background (CORSIKA-SIBYLL,iron) and signal (GZK 1 [3]) Monte Carlo simulations
following a blind analysis strategy. The minimum NPE

TABLE I. Number of events passing cuts at various selection levels with 333.5 days detector live time. The signal rates correspond tosimulations of the GZK 1 model [3]. The errors of the online, offline and quality bright samples are statistical only. Systematic
uncertainties in the expected event rates at the final selection level are given as asymmetric error intervals after the statistical error.
Samples

Experimental

Background MC (SIBYLL, iron)Signal MC (GZK 1)

On-lineOff-line

3:7  107

ð3:8  0:1Þ  107

1:8  0:007
1:2  0:006

QualityFinal

3:3  105
ShallowDeep
1:9  103
2:9  10500

ð4:8  0:2Þ  105
ShallowDeepð4:4  0:2Þ  105
ð1:7  0:2Þ  103
0:032  0:010þ0:022
0:076  0:012þ0:051
0:032
0:075092003-5

Shallow
0:76  0:005
0:39  0:004þ0:054
0:043

Deep
0:43  0:004
þ0:025
0:18  0:0020:020

R. ABBASI et al.

PHYSICAL REVIEW D 83, 092003 (2011)

threshold value is 2:5  10 . Events with NPE above thethreshold value in each bin are considered to be signal event
candidates. No events above the threshold are found in the
10% subset of the experimental sample. Monte Carlo simulations indicate that a cosmic-ray primary energy of at least2  109 GeV is required for a muon bundle to be selected
as the final sample. Table I summarizes the number of
events retained in each level of analysis.
4

IV. THE SYSTEMATICS
Table II summarizes the sources of statistical and systematic errors in signal and background. The systematic
uncertainties are assumed to have a flat distribution and aresummed in quadrature separately for background andsignal.
The dominant source of systematic uncertainty in thesignal event rate is the relationship between the measured
NPE and the energy of the charged particles. The uncertainty is estimated by calibrating the absolute sensitivity of
the DOMs in the laboratory and by calibrating the in-situ
sensitivity using light sources codeployed with the DOMs
in the ice. The estimation by the latter method involves
systematic errors in the simulation of the photon propagation in the ice. The uncertainty associated with possible
underestimation in the DOM’s random noise is estimatedby adding artificial random photoelectrons into 10% of thesimulated events. The other uncertainties attributed to theneutrino interactions [27] and their daughters’ interactionsin the ice are similarly estimated as in the previous
analysis [13].
TABLE II. List of the statistical and systematic errors for
signal (top) and background (bottom) simulations. The uncertainties for the signal are listed relative to the rate estimated for
GZK 1 [3]. The uncertainties in the signal rates vary withassumed signal spectra. The uncertainties in the backgroundrate are estimated with CORSIKA-SIBYLL assuming iron composition.
Sources

Signal rate (%)

Statistical error
NPE
Noise
Neutrino cross section
Photo-nuclear interaction
Landau-Pomeranchuk-Migdal effect0:8
þ3:9=  7:2
1:8
9:0
þ10:0
1:0

Total:

0:8ðstatÞ þ 14:0  11:7ðsysÞ

Sources

Background rate (%)

Statistical error
NPE
Noise
Cosmic ray composition
Hadronic interaction model
Coincident events
Total:

17:0
þ37:1=  46:7
2:2
83:9
þ36:1
þ31:2
17:0ðstatÞ þ 60:4  96:0ðsysÞ

The dominant source of systematic uncertainty in the
background event rates arises from the uncertainty in the
primary cosmic-ray composition at the relevant energies( > 107 GeV) and the hadronic interaction model used in
the simulation of the air showers. The systematic uncertainty associated with the cosmic-ray composition is evaluated by considering two extreme cases of atmosphericmuon simulations with either pure iron or pure proton
primary compositions. Similarly, the uncertainty due tothe hadronic interaction model is evaluated using atmospheric muon simulations with two different high energy
hadronic interaction models: SIBYLL 2.1 and QGSJET-II.
Systematic uncertainties associated with the NPE measurement and the possible DOM noise rate underestimation aredetermined in the same manner as for signal events. The
background contribution from possible prompt muons created in decays of charmed mesons is negligible. There isalso uncertainty due to statistical limitations of the simulated coincident muon sample at NPE  104 . This error isestimated by extrapolating distributions of statisticallyricher lower NPE coincident simulation events to the final
selection region. Possible coincident events in the final
sample are also estimated by the temporally and geometrically separated p.e. signals from the main p.e. cluster ineach event. This coincident event check suggested that oneof the two upward-going reconstructed events in Fig. 1(b)at cos ¼ 0:38 was due to coincident muons. The otherupward-going event ( cos ¼ 0:83) was possibly
neutrino-induced, while the NPE values of both eventswere approximately 4300 p.e., a factor of 6 less than the
final threshold value.
V. RESULTS
No events in the blinded 90% experimental data pass all
the selection criteria. This is consistent with the expectedbackground level of 0:11  0:02þ0:06
0:10 events in a live timeof 333.5 days. The passing rates for experimental andsimulated events at each selection level are listed inTable I.
The quasidifferential model-independent 90% CL limit
on neutrino fluxes [28] normalized by energy decade isshown in Fig. 3 assuming full mixing in the standard
neutrino flavor oscillation scenario. In the limit calculation,
the energy decade averaged effective area is used and thecontribution from the Glashow resonance [29] is neglected.
Incorporating the statistical and systematic uncertainties,
the background is expected to be found with a uniform
prior probability between 0 and 0.19. These uncertainties
are included in the final limit using a method outlined in[30]. This estimation together with the null result in theexperimental sample gives the Feldman-Cousins 90% CL
event upper limit [31] of 2.35 events. For cosmic neutrinos
with an E2 energy spectrum, this implies an integral flux
limit of E2   3:6  108 GeV cm2 sec1 sr1 with thecentral 90% of the E2 signal found in the energy interval

092003-6

CONSTRAINTS ON THE EXTREMELY-HIGH ENERGY . . .
-4
10-4

PHYSICAL REVIEW D 83, 092003 (2011)
106

106

(a)

GZK 1

(b)

GZK 4
GZK 5

-6
10-6

WB bound

-8

10-8

1

104

102

1

IC-40 (333.5 days)
the full IceCube(3 years)

IC-22

10-2

ANITA

-9

10

7

PAO

8

9

7

8

log Eν e /GeV

(c)

10
104

FIG. 3 (color online). All flavor neutrino flux differential limit
and E2 spectrum integrated limit from the 2008-2009 IceCube
EHE analysis (bold solid lines). The systematic errors areincluded. Various model predictions (assuming primary protons)
are shown for comparison: GZK 1 (ðm; Zmax Þ ¼ ð4; 4Þ) [3], GZK
2 [4], GZK 3 ( ¼ 0:0), GZK 4 ( ¼ 0:7) [5], GZK 5(maximal) and GZK 6 (the best fit, incorporating the FermiLAT bound) [6]. The gray dashed horizontal line indicates the
Waxman-Bahcall flux bound with cosmological evolution [32].
Model fluxes are summed over all neutrino flavors, assuming
standard neutrino oscillations. The model-independent differential upper limits by other experiments are also shown for Auger(PAO) [8], RICE [9], ANITA [11], and the previous IceCube
result (IC22) [13]. Limits from other experiments are converted
to the all flavor limit assuming standard neutrino oscillation anda 90% quasidifferential limit when necessary. The integral flux
limit on a pure E2 spectrum is shown for AMANDA-II [12].
For reference, the estimated integrated limit for three years ofobservation with the full IceCube detector with the same analysis
strategy is denoted as a gray solid line.

2:0  106  6:3  109 GeV. This result is the first constraint of neutrino fluxes below the Waxman-Bahcall (WB)
flux bound [32] in this energy region.
VI. DISCUSSIONS AND SUMMARY
We analyzed the 2008-09 data sample collected by the
40-string IceCube detector to search for extremely-highenergy neutrinos with energies exceeding 106 GeV. The
differential and integral limits obtained are significantly
improved relative to our previous result [13]. This is due toboth the increased instrumented volume and improvementsof the Monte Carlo simulations. The improved agreement
between experimental and simulated data allowed a loosening of the NPE threshold in the data selection, thereby
lowering the energy threshold of the analysis and improving the selection efficiency for high energy signal events
that occurred outside the instrumented volume. This canalso be seen in the corresponding neutrino effective area atthe final selection shown in Fig. 4. Compared to theντ Effective Area [m2]8102

zenith angle (0o, 60o)
zenith angle (60o, 90o)
zenith angle (90o, 150o)
zenith angle (150o, 180o)zenith angle (0o, 180o)

1

10-2

7

8

9

log10Eν τ /GeV

10

(d)

νe + νeνµ + νµ0.025

log10(Energy/GeV)

10

10

106

6

9

log Eνµ /GeV

10

RICE

4

10-2

10

AMANDA

-10

-10
10

102

Number of Events

10-7

GZK 6

104

νµ Effective Area [m2]

GZK 3

10-5

νe Effective Area [m2]E2 φ(E) [GeV cm-2 sec-1 sr-1]

GZK 2

ντ + ντ

0.02

0.015

0.01

0.005

0

5

6

7
log

8
10

9

10

11

Eν /GeV

FIG. 4 (color online). Solid angle averaged neutrino effective
area for four declination bands as well as that of the full solid
angle average for (a) e þ  e (b)  þ   and (c)  þ   ,assuming equal flux of neutrinos and antineutrinos. The lower
right plot shows the final level signal event distributions for333.5 days with the GZK 6 model spectra [6] for each neutrino
flavor.

previous search [13], the effective area is a factor of 6
and 3.3 increased at 3  107 GeV and 109 GeV, respectively. The full solid angle averaged 3 flavor (assuminge : : : ¼ 1:1:1) neutrino effective area reaches 300 m2
at 108 GeV and 2100 m2 at 109 GeV. The 90% CL differential limit at 109 GeV is a factor of 4 higher than thefluxes predicted by the models GZK 2 and 5, and a factor of8 higher than the flux predicted by the models GZK 1, 4,
6, all of which assume primary protons. This suggests that
the IceCube EHE neutrino search will reach these flux
levels in the near future since the event rate is roughly
proportional to the fiducial volume (see Fig. 3), and thecurrent analysis used only the half-instrumented IceCube
detector configuration. Further improvements in sensitivity
would enable IceCube to act as a probe of the primarycosmic ray composition at GZK energies [33].
Figure 4 indicates that a large part of the EHE neutrinosignal is expected from the zenith angle region between
60 and 90. Upward-going EHE neutrinos are absorbed in
the Earth. The propagation length of secondary muons andtaus is greater than the distance between the surface and the
IceCube fiducial volume. Thus, the inclined particles thatreach the IceCube detector are created in the Earth. For e ,092003-7

R. ABBASI et al.

PHYSICAL REVIEW D 83, 092003 (2011)

TABLE III. Expected number of events in 333.5 days fromseveral cosmogenic neutrino models and top-down models. The
confidence interval for exclusion by this observations is also
listed where appropriate. The cosmogenic neutrino models(GZK 1-6) assume the cosmic-ray primaries to be protons anddifferent spectral indices/cutoff energies at sources as well as
different cosmological evolution parameters and extension inredshift for the sources. Representative models with moderate(GZK 3, 4, 6), moderately strong (GZK 1) and strong (GZK 2, 5)
source evolution parameters are listed here.
ModelsGZK 1 [3]GZK 2 [4]GZK 3 ( ¼ 0:0) [5]
GZK 4 ( ¼ 0:7) [5]
GZK 5 (maximal) [6]
GZK 6 (the best fit) [6]Top-down 1 (SUSY) [22]Top-down 2 (no-SUSY) [22]Z-burst [21]WB bound (with evolution) [32]
WB bound (without evolution) [32]Event rate

C.L. %

0.57
0.91
0.29
0.47
0.89
0.43
1.0
5.7
1.2
4.5
1.0


53.4


52.8

55.7
99.6
66.4



cosmogenic neutrinos, top-down scenarios, and a pure E2
power-law neutrino spectrum normalized to the WaxmanBahcall flux bounds for reference. We expect 0.3 to 0.9
cosmogenic neutrino events in 333.5 days, assuming moderate to strong cosmological source evolution models. The
half-instrumented IceCube detector is already capable ofconstraining those models with relatively high neutrino
fluxes. The IceCube sensitivity to cosmological EHE neutrinos continues to grow.
ACKNOWLEDGMENTS

the event signatures are produced nearly at the neutrino
interaction points and the current analysis is sensitive to all
downward-going geometries. The peaked features in Fig. 4(a) and 4(d) at Ee  6:3 PeV are due to the Glashow
resonance [29]. Expected signal energy distributions of
GZK 6 at the final selection level are shown in the lower
right panel in Fig. 4. The peak energy of the expectedsignal after all selection criteria is at 7:0  108 GeV.
Significant contributions from all neutrino flavors are observed. In the GZK 6 model, 13% of the signal are from e ,45% are from  and 42% are from  . Through-goingtracks (muons and taus) constitute 60% of the signal
rate and the rest are neutrino interactions that create
cascadelike events near and inside the detector volume.
Table III gives the event rates for several model fluxes ofWe acknowledge the support from the following agencies: U.S. National Science Foundation-Office of Polar
Programs, U.S. National Science Foundation-Physics
Division, University of Wisconsin Almni Research
Foundation, the Grid Laboratory Of Wisconsin (GLOW)
grid infrastructure at the University of Wisconsin Madison, the Open Science Grid (OSG) grid infrastructure;
U.S. Department of Energy, and National Energy Research
Scientific Computing Center, the Louisiana Optical
Network Initiative (LONI) grid computing resources;
National Science and Engineering Research Council of
Canada; Swedish Research Council, Swedish Polar
Research Secretariat, Swedish National Infrastructure for
Computing (SNIC), and Knut and Alice Wallenberg
Foundation, Sweden; German Ministry for Education andResearch (BMBF), Deutsche Forschungsgemeinschaft(DFG), Research Department of Plasmas with Complex
Interactions (Bochum), Germany; Fund for Scientific
Research (FNRS-FWO), FWO Odysseus programme,
Flanders Institute to encourage scientific and technologicalresearch in industry (IWT), Belgian Federal Science Policy
Office (Belspo); University of Oxford, United Kingdom;
Marsden Fund, New Zealand; Japan Society for Promotionof Science (JSPS); the Swiss National Science Foundation(SNSF), Switzerland; A. Groß acknowledges support by
the EU Marie Curie OIF Program; J. P. Rodrigues acknowledges support by the Capes Foundation, Ministry of
Education of Brazil.

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