IceCube 論文集出版にあたって
IceCube12
GZK

IceCubeIceCubeIceCubeIceCube

2014

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It has been a dozen of years since the IceCube international collaboration was organized. We, the IceCube
group from Chiba University, have been engaged in searches of ultra-high energy neutrinos, our ﬂagship mission,
which leads to understanding of the origin of the highest energy cosmic rays. Our group has been deeplycommitted the ﬁrst observational evidence of existence of a high energy astrophysical neutrino ﬂux, and theconsequent achievement of sensitivity good enough to make a detection of ”cosmogenic” neutrinos a reality. On
this occasion, we would like to share the obtained scientiﬁc knowledges with you by publishing this collectionof papers.
The IceCube collaboration has published numerous papers. This collection picked up the ones the Japanʼsgroup has greatly contributed to. The papers published with authors of an individual member from the groupare also included among them. It is my pleasure if this series of papers presents to you how neutrinos canprobe the ultra-high energy Universe and their great potential to ﬁnally resolve the long-standing mystery of
the ultra-high energy comic-ray origin.
An every each of the achievements collected here has relied on a power of team work. It is very fortunatethat my team is ﬁlled with so talented associates. They are really amazing, not just as a member of the team,
but also as an independent scientist. None of the papers listed here could have been published without them.
And moreover, collaborations with IceCube colleagues from all over the world are indispensable foundations
to all the achievements my group has fortunately made. It has been really a fun to work on IceCube with mycollaborators in many countries.
A basic science mission like the IceCube project requires a lengthy and time-consuming process to get
ready for producing scientiﬁc results. We have had to survive a long diﬃcult time when there was no chance towrite any single science paper. I really appreciated all of you who have encouraged us during this ”predawn”
period, trusting our capability to produce something important to particle astrophysics in near future. Ourjourney still goes on. I have no doubt that even more amazing discoveries are following. Stay tuned!

Shigeru Yoshida
Chiba City, Japan
Feburuary 3, 2014.

目

次

CONTENTS"Probing the origin of cosmic rays with extremely high energy neutrinos using the IceCube Observatory"(IceCube collaboration) ·············································································································

1

PeV ニュートリノ事象を発見した超高エネルギー宇宙ニュートリノ探索解析の詳細報告。解析から得られた 100PeV 以上の超高エネルギ
ー領域での宇宙ニュートリノ流量の最も厳しい上限値から、超高エネルギー宇宙線源の性質に重要な制限を与えた。ニュートリノ観測結果から超高エネルギー宇宙線起源に関する天体物理学的に有意義な知見を初めて与えた成果である。2013 年出版。
The detailed report on the extremely-high energy cosmic neutrino searches leading to the discovery of the two PeV-Energy neutrinos. The analysis
placed the strong limit on the neutrino fluxes in the energy range above 100 PeV. The limit constrains the important region of the parameter spaceconcerning the characteristics of the highest energy cosmic-ray sources. This paper represents the first achievement that neutrino observations haveindeed provided astrophysically important implications on the origin of ultra-high energy cosmic rays. Published in 2013.

"First Observation of PeV-Energy Neutrinos with IceCube"(IceCube collaboration) ············································································································· 16
千葉大グループが推進してきた超高エネルギー宇宙ニュートリノ探索によって発見された PeV のエネルギーを持つニュートリノ事象発見の報告。このエネルギーは観測史上最高エネルギーであり、高エネルギー宇宙ニュートリノが存在することを最初に実験的に示唆した記念碑的論文。2013 年出版。
The report on the observation of PeV-Energy neutrinos discovered by the ultra-high energy cosmic neutrino search, the program the Chiba IceCube
group has been promoting since its beginning. Their energies are the highest observed so far. It is the monumental paper to describe the very firstexperimental indication of the existence of an astrophysical neutrino flux. Published in 2013.

"Constraints on the origin of the ultrahigh energy cosmic rays using cosmic diffuse neutrino flux limits: An analytical
approach"(Shigeru Yoshida and Aya Ishihara) ································································································ 23
宇宙背景輻射との衝突で生じるニュートリノ流量を解析的に算出する手法を導出し、ニュートリノ流量上限値を超高エネルギー宇宙線源の性質の制限に変換する処方を示した。近い将来この方法によって IceCube 実験は超高エネルギー宇宙線源に関する有意義な知見をもたらすことを論じた。2012 年出版。
Presented the semi-analytic formula to calculate fluxes of cosmogenic neutrinos produced by the collisions with the CMB. It provides the recipe to
extract bounds on the characteristics of the ultra-high energy cosmic-ray sources from the limits on the neutrino fluxes. It was discussed that the future
limits from the IceCube detector is able to fruitfully constrain the ultra-high energy cosmic ray sources. Published in 2012.

"Constraints on the extremely-high energy cosmic neutrino flux with the IceCube 2008-2009 data"(IceCube collaboration) ············································································································· 32
超高エネルギ領域(PeV-EeV)で世界で最も厳しい宇宙ニュートリノ流量上限値を出した解析結果。約半分の検出器が埋設・運転された
2008-2009 年のデータによる。IceCube 実験が EeV 領域で世界一の感度を持つことを示した節目の論文。超高エネルギー宇宙線の素粒子
物理的起源説に極めて厳しい制限を与えている。2011 年出版。
The analysis placing the most stringent bound on the cosmic neutrino flux in ultra-high energy region (PeV-EeV). Based on the data taken with thehalf-constructed IceCube detector collected between April 2008 and May 2009. It is the milestone paper demonstrating that IceCube provides the world
No.1 sensitivity in EeV range. It places the strong constraints on the particle physics-oriented scenarios on the origin of high energy cosmic rays.
Published in 2011.

"Constraints on neutrino-nucleon interactions at energies of 1 EeV with the IceCube Neutrino Observatory"(Shigeru Yoshida) ··················································································································· 41
超高エネルギー領域における IceCube 実験の data はニュートリノ・核子相互作用断面積の上限値を決めることによって標準理論を超える素粒子物理の枠組みに制限を加え得ることを示した。2010 年出版。
It demonstrated that the data in ultra-high energy region from the IceCube is capable of constraining new particle physics that enhances theneutrino-nucleon interaction cross section. A bound in the parameter space of the black hole creation as a possible consequence of low-scale gravity was
obtained. Published in 2010.

"First search for extremely high energy cosmogenic neutrinos with the IceCube Neutrino Observatory"(IceCube Collaboration) ············································································································ 47
IceCube 実験で可能な最も高エネルギー領域における宇宙ニュートリノ探索をターゲットに掲げている千葉大学グループによる最初の物理論文。全検出器の約 1/4 が埋設され稼働していた。2007 年時のデータによる。IceCube 実験がメインエネルギー領域である TeV だ
けではなく PeV-EeV 領域でも競争力があることを示した。2010 年出版。
The first physics analysis paper written by the Chiba group who has been targeting searches of the cosmic neutrinos at the highest energies beyond PeV
for a primary physics program. Based on the data taken by the partially (approximately a quater) constructed IceCube in 2007. It demonstrated that
IceCube is competitive not only in TeV regime, the main energy range of the project, but also in PeV-EeV regime where the GZK cosmogenic neutrinos
are expected to exist. Published in 2010.

"Calibration and characterization of the IceCube photomultiplier tube"(IceCube Collaboration) ············································································································ 58
IceCube 実験の基幹デバイスである光電子増倍管の応答測定及びキャレーブレーション結果。このデバイスの測定に責任を持っていた千葉大学グループの実験建設時における主要な寄与であった。IceCube 実験の全ての物理解析の基礎を与える論文の一つ。2010 年出版。
The laboratory characterization and calibration of the PMTs, the key device, in the IceCube experiment. This paper represents the major contributionsof the Chiba group who had been in charge of the PMT measurements during the detector construction phase. This is one of the papers which provide
foundations for all physics analyses with the IceCube detector. Published in 2010.

宇宙ニュートリノ初公表時のスライド
The presentation slide of the 1st annoucement on the detection of the cosmic neutrino event candidates. ················ 72

写真集
A collection of photographs ·········································································································· 73

PHYSICAL REVIEW D 88, 112008 (2013)

Probing the origin of cosmic rays with extremely high energy neutrinos
using the IceCube Observatory
M. G. Aartsen,2 R. Abbasi,29 M. Ackermann,45 J. Adams,15 J. A. Aguilar,23 M. Ahlers,29 D. Altmann,22 C. Arguelles,29
J. Auffenberg,29 X. Bai,33,* M. Baker,29 S. W. Barwick,25 V. Baum,30 R. Bay,7 J. J. Beatty,17,18 J. Becker Tjus,10
K.-H. Becker,44 S. BenZvi,29 P. Berghaus,45 D. Berley,16 E. Bernardini,45 A. Bernhard,32 D. Z. Besson,27 G. Binder,8,7
D. Bindig,44 M. Bissok,1 E. Blaufuss,16 J. Blumenthal,1 D. J. Boersma,43 C. Bohm,36 D. Bose,38 S. Böser,11 O. Botner,43
L. Brayeur,13 H. -P. Bretz,45 A. M. Brown,15 R. Bruijn,26 J. Casey,5 M. Casier,13 D. Chirkin,29 A. Christov,23 B. Christy,16
K. Clark,39 F. Clevermann,20 S. Coenders,1 S. Cohen,26 D. F. Cowen,42,41 A. H. Cruz Silva,45 M. Danninger,36
J. Daughhetee,5 J. C. Davis,17 M. Day,29 C. De Clercq,13 S. De Ridder,24 P. Desiati,29 K. D. de Vries,13 M. de With,9T. DeYoung,42 J. C. Dı́az-Vélez,29 M. Dunkman,42 R. Eagan,42 B. Eberhardt,30 J. Eisch,29 S. Euler,1 P. A. Evenson,33
O. Fadiran,29 A. R. Fazely,6 A. Fedynitch,10 J. Feintzeig,29 T. Feusels,24 K. Filimonov,7 C. Finley,36 T. Fischer-Wasels,44
S. Flis,36 A. Franckowiak,11 K. Frantzen,20 T. Fuchs,20 T. K. Gaisser,33 J. Gallagher,28 L. Gerhardt,8,7 L. Gladstone,29
T. Glüsenkamp,45 A. Goldschmidt,8 G. Golup,13 J. G. Gonzalez,33 J. A. Goodman,16 D. Góra,22 D. T. Grandmont,21
D. Grant,21 P. Gretskov,1 J. C. Groh,42 A. Groß,32 C. Ha,8,7 A. Haj Ismail,24 P. Hallen,1 A. Hallgren,43 F. Halzen,29
K. Hanson,12 D. Heereman,12 D. Heinen,1 K. Helbing,44 R. Hellauer,16 S. Hickford,15 G. C. Hill,2 K. D. Hoffman,16
R. Hoffmann,44 A. Homeier,11 K. Hoshina,29 W. Huelsnitz,16 P. O. Hulth,36 K. Hultqvist,36 S. Hussain,33 A. Ishihara,14,†
E. Jacobi,45 J. Jacobsen,29 K. Jagielski,1 G. S. Japaridze,4 K. Jero,29 O. Jlelati,24 B. Kaminsky,45 A. Kappes,22 T. Karg,45
A. Karle,29 M. Kauer,29 J. L. Kelley,29 J. Kiryluk,37 J. Kläs,44 S. R. Klein,8,7 J.-H. Köhne,20 G. Kohnen,31 H. Kolanoski,9
L. Köpke,30 C. Kopper,29 S. Kopper,44 D. J. Koskinen,19 M. Kowalski,11 M. Krasberg,29 A. Kriesten,1 K. Krings,1G. Kroll,30 J. Kunnen,13 N. Kurahashi,29 T. Kuwabara,33 M. Labare,24 H. Landsman,29 M. J. Larson,40 M. Lesiak-Bzdak,37
M. Leuermann,1 J. Leute,32 J. Lünemann,30 O. Macı́as,15 J. Madsen,35 G. Maggi,13 R. Maruyama,29 K. Mase,14,‡
H. S. Matis,8 F. McNally,29 K. Meagher,16 M. Merck,29 T. Meures,12 S. Miarecki,8,7 E. Middell,45 N. Milke,20 J. Miller,13
L. Mohrmann,45 T. Montaruli,23,§ R. Morse,29 R. Nahnhauer,45 U. Naumann,44 H. Niederhausen,37 S. C. Nowicki,21
D. R. Nygren,8 A. Obertacke,44 S. Odrowski,21 A. Olivas,16 A. Omairat,44 A. O’Murchadha,12 L. Paul,1 J. A. Pepper,40
C. Pérez de los Heros,43 C. Pfendner,17 D. Pieloth,20 E. Pinat,12 J. Posselt,44 P. B. Price,7 G. T. Przybylski,8 L. Rädel,1
M. Rameez,23 K. Rawlins,3 P. Redl,16 R. Reimann,1 E. Resconi,32 W. Rhode,20 M. Ribordy,26 M. Richman,16 B. Riedel,29
J. P. Rodrigues,29 C. Rott,38 T. Ruhe,20 B. Ruzybayev,33 D. Ryckbosch,24 S. M. Saba,10 H. -G. Sander,30 M. Santander,29
S. Sarkar,34 K. Schatto,30 F. Scheriau,20 T. Schmidt,16 M. Schmitz,20 S. Schoenen,1 S. Schöneberg,10 A. Schönwald,45
A. Schukraft,1 L. Schulte,11 O. Schulz,32 D. Seckel,33 Y. Sestayo,32 S. Seunarine,35 R. Shanidze,45 C. Sheremata,21
M. W. E. Smith,42 D. Soldin,44 G. M. Spiczak,35 C. Spiering,45 M. Stamatikos,17,∥ T. Stanev,33 N. A. Stanisha,42
A. Stasik,11 T. Stezelberger,8 R. G. Stokstad,8 A. Stößl,45 E. A. Strahler,13 R. Ström,43 G. W. Sullivan,16 H. Taavola,43
I. Taboada,5 A. Tamburro,33 A. Tepe,44 S. Ter-Antonyan,6 G. Tešić,42 S. Tilav,33 P. A. Toale,40 M. N. Tobin,29 S. Toscano,29
E. Unger,10 M. Usner,11 S. Vallecorsa,23 N. van Eijndhoven,13 A. Van Overloop,24 J. van Santen,29 M. Vehring,1 M. Voge,11
M. Vraeghe,24 C. Walck,36 T. Waldenmaier,9 M. Wallraff,1 Ch. Weaver,29 M. Wellons,29 C. Wendt,29 S. Westerhoff,29
N. Whitehorn,29 K. Wiebe,30 C. H. Wiebusch,1 D. R. Williams,40 H. Wissing,16 M. Wolf,36 T. R. Wood,21 K. Woschnagg,7
D. L. Xu,40 X. W. Xu,6 J. P. Yanez,45 G. Yodh,25 S. Yoshida,14,¶ P. Zarzhitsky,40 J. Ziemann,20 S. Zierke,1 and M. Zoll36(IceCube Collaboration)
1
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
School of Chemistry & Physics, University of Adelaide, Adelaide, South Australia 5005, Australia
3
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Drive, Anchorage, AK 99508, USA
4
CTSPS, Clark-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
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
13
Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
21550-7998= 2013=88(11)=112008(15)112008-1

Ó 2013 American Physical Society

1M. G. AARTSEN et al.

PHYSICAL REVIEW D 88, 112008 (2013)14

Department of Physics, Chiba University, Chiba 263-8522, Japan
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
16
Department of Physics, University of Maryland, College Park, Maryland 20742, USA
17
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210, USA
18
Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA
19
Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
20
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germany
21
Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1
22Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
23
Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
24
Department of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
25
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
26
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland
27
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
28
Department of Astronomy, University of Wisconsin, Madison, Wisconsin 53706, USA
29
Department of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, Wisconsin 53706, USA
30
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
31
Université de Mons, 7000 Mons, Belgium
32
T.U. Munich, D-85748 Garching, Germany
33
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
34
Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
35
Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA
36
Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
37
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
38
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
39
Department of Physics, University of Toronto, Toronto, Ontario, Canada, M5S 1A7
40
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA
41
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
42
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
43
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
44
Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
45
DESY, D-15735 Zeuthen, Germany(Received 20 October 2013; published 16 December 2013)15

We have searched for extremely high energy neutrinos using data taken with the IceCube detector
between May 2010 and May 2012. Two neutrino-induced particle shower events with energies around 1 PeV
were observed, as reported previously. In this work, we investigate whether these events could originate fromcosmogenic neutrinos produced in the interactions of ultrahigh energy cosmic rays with ambient photons
while propagating through intergalactic space. Exploiting IceCube’s large exposure for extremely highenergy neutrinos and the lack of observed events above 100 PeV, we can rule out the corresponding models
at more than 90% conﬁdence level. The model-independent quasidifferential 90% C.L. upper limit, whichamounts to E2 e þ þ ¼ 1:2  107 GeV cm2 s1 sr1 at 1 EeV, provides the most stringent constraint
in the energy range from 10 PeV to 10 EeV. Our observation disfavors strong cosmological evolution of thehighest energy cosmic-ray sources such as the Fanaroff-Riley type II class of radio galaxies.
DOI: 10.1103/PhysRevD.88.112008

PACS numbers: 98.70.Sa, 95.85.Ry, 95.55.Vj

I. INTRODUCTION*Also at Physics Department, South Dakota School of Mines
and Technology, Rapid City, SD 57701, USA.
†
Corresponding author.
aya@hepburn.s.chiba-u.ac.jp‡
Corresponding author.
mase@hepburn.s.chiba-u.ac.jp§
Also at Sezione INFN, Dipartimento di Fisica, I-70126, Bari,
Italy.
∥
Also at NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA.
¶
Corresponding author.
syoshida@hepburn.s.chiba-u.ac.jp

Cosmic neutrinos are expected to be produced in theinteractions of high energy hadronic particles from cosmic
accelerators with surrounding photons and matter. At PeV
energies or greater, neutrinos are a unique tool for the
direct survey of the ultrahigh energy universe, because
photons at these energies are highly attenuated by thecosmic microwave background (CMB). In addition to neutrinos directly produced in cosmic-ray sources, secondary
neutrinos produced in the propagation of ultrahigh energy
cosmic rays (UHECRs) with energies reaching about

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PHYSICAL REVIEW D 88, 112008 (2013)

100 EeV are expected. These ‘‘cosmogenic’’ neutrinos areproduced by the Greisen-Zatsepin-Kuzmin (GZK) mechanism via interactions of UHECRs with the CMB andextragalactic background light (infrared, optical, and ultraviolet) [1–3]. A measurement of cosmogenic (or GZK)
neutrinos probes the origin of the UHECRs because thespectral shapes and ﬂux levels are sensitive to the redshiftdependence of UHECR source distributions and cosmicray primary compositions [4,5]. Neutrinos are ideal particles to investigate the origin of UHECRs since neutrinos
propagate to the Earth essentially without deﬂection andabsorption. The main energy range of the cosmogenic
neutrinos is predicted to be around 100 PeV–10 EeV[6,7]. In this extremely high energy (EHE) region, cosmogenic production is considered the main source of cosmic
neutrinos.
A measurement of these EHE neutrinos requires a detection volume on the order of at least 1 km3 as their ﬂuxes
are expected to be very low, yielding approximately one
event per year in such a volume [8,9]. The IceCube
Neutrino Observatory [10] at the geographical South Poleis the ﬁrst cubic-kilometer scale neutrino detector. Its large
instrumented volume as well as its omnidirectional neutrino detection capability have increased the sensitivity for
EHE cosmogenic neutrinos signiﬁcantly. Previous EHE
neutrino searches performed with IceCube [9,11] showedthat IceCube has become the most sensitive neutrino
detector in the energy range of 1 PeV–10 EeV compared
to experiments using other techniques [12–16]. The sensitivity of the complete IceCube detector reaches to themodestly high ﬂux cosmogenic models which assume apure proton composition of cosmic rays. The ﬂux for aheavier composition such as iron is at least 2–3 times
lower, although the decrease depends on the source evolution [17] and strongly on the maximal injection energy ofthe sources [18]. In order to test the heavier composition
model predictions, longer exposure or other detection
techniques such as the radio detection are needed.
The EHE neutrino search presented here uses dataobtained from May 2010 to May 2012. The analysis issensitive to all three neutrino ﬂavors. The basic searchstrategies are similar to previous searches [9,11]. The
main improvement comes from the enlargement of thedetector and the statistical enhancement of the data as
well as improved modeling of optical properties of the
deep glacial ice [19] in the Monte Carlo simulations. The
improvements allow a reﬁned geometrical reconstructionof background events and thus a better background rejection. Two neutrino-induced PeV-energy particle shower
events were discovered by this EHE neutrino analysis asreported in Ref. [20]. In this paper, we describe the detailsof the analysis. Then, we investigate whether the two
observed events are consistent with cosmogenic neutrinos.
Afterwards, cosmogenic neutrino models are tested forcompatibility with our observation in order to constrain
the UHECR origin.

The paper is structured as follows: In Secs. II and III, the
IceCube detector and the data samples are described. The
improved analysis methods and the associated systematic
uncertainties are discussed in Secs. IV and V. In Sec. VI,
results from the analysis are presented. Implications of theobservational results on the UHECR origin are discussed inSec. VII by testing several cosmogenic neutrino models.
The model-independent upper limit of the EHE neutrino
ﬂux is shown in Sec. VIII. Finally, the results are summarized in Sec. IX.
II. THE IceCube DETECTORThe IceCube detector observes the Cherenkov light fromthe relativistic charged particles produced by high energy
neutrino interactions using an array of digital opticalmodules (DOMs). Each DOM comprises a 10’’ R708102 photomultiplier tube (PMT) [21] in a transparent pressure sphere along with a high voltage system, a digital
readout board [22], and a LED ﬂasher board for opticalcalibration in ice. These DOMs are deployed along electrical cable bundles that carry power and information
between the DOMs and the surface electronics. The cable
assemblies called strings were lowered into holes drilled toa depth of 2450 m with a horizontal spacing of approximately 125 m (Fig. 1). The DOMs sit where the glacial ice
is transparent at depths from 1450 to 2450 m at intervals of
17 m. PMT waveforms are recorded when the signal in a
DOM crosses a threshold and the nearest or next-to-nearest
DOM observes a photon within 1 s (hard local coincidence, HLC). An event is triggered if eight DOMs record a
HLC within 5 s. The lower, inner part of the detector
called DeepCore [23] is ﬁlled with DOMs with a smaller
vertical and horizontal spacing of 7 and 72 m, respectively.
The DeepCore array is mainly responsible for the enhancement of the performance below 100 GeV, the thresholdenergy of IceCube. Additional DOMs frozen into tanks

FIG. 1 (color online). A schematic view of the IceCube
detector.

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PHYSICAL REVIEW D 88, 112008 (2013)

located at the surface near the top of each hole constitute an
air shower array called IceTop [24]. IceTop allows for the
study of cosmic-ray physics and provides the capability to
study the atmospheric muon background. The whole detector system comprises 5160 DOMs on 86 strings out of
which eight strings correspond to DeepCore, and an additional 324 DOMs in the surface array. The conﬁgurationsof the IceCube detectors are displayed in Fig. 1.
III. DATA AND SIMULATIONThe IceCube detector construction was completed in
December, 2010. During the construction phase, fromMay 31, 2010 to May 12, 2011, 79 strings (IC79), approximately 90% of the full detector, were operational. The IC79
run was immediately followed by the ﬁrst year of datataking with the full detector (IC86) which lasted fromMay 13, 2011 to May 15, 2012. The data from these periods
were used in this analysis. The corresponding live time for
the IC79 and IC86 runs were 319.2 days and 350.9 days
respectively, excluding periods of detector calibration andunstable operation. Approximately 10% of the sample(33.4 days of IC79 and 20.8 days of IC86 running) wasused as a statistically independent test sample for veriﬁcation. The ﬁnal analysis was performed in a blind way where
the test sample was not used for the signal search.
There are two classes of background events: atmospheric muon bundle events and events induced by atmospheric neutrinos. Muon bundles consist of a large numberof high energy muons produced by cosmic-ray interactionsin the atmosphere. Regardless of their high muon multiplicities, they are observed as a single track since theirlateral separations of about 10 m is shorter than the minimum DOM separation of 17 m except for DeepCore. Since
the detector is large and the data recording time window isalso long (10 s), there is a non-negligible chance that two
or more muon bundles arrive at the same time. These
events called ‘‘coincident events’’ complicate geometricalreconstruction. Special treatment is required to reduce thisbackground. Atmospheric muon bundles were simulatedwith the CORSIKA air shower simulation [25] with the
SIBYLL 2.1 hadronic interaction model [26]. Muons fromthe showers were propagated from the Earth’s surface to
IceCube depths with the Muon Monte Carlo package [27].
These were the same programs as in previous studies [9]except that we have improved our description of the opticalproperties of the glacier ice [19] used in the simulation of
the photon propagation from the particles to the DOMs.
For the atmospheric neutrinos, the All Neutrino
Interaction Simulation package [28] was used to simulate
each neutrino ﬂavor separately between 50 GeV and 1 EeV.
The neutrino events were simulated following an E1
spectrum on the surface of the Earth with appropriate
ﬂux weights to represent the spectrum resulting fromdecays of cosmic-ray-induced pions and kaons in theatmosphere (‘‘conventional’’ atmospheric neutrinos). We

use the cosmic-ray spectrum modeled in Ref. [29] to take
into account the spectral bend at the cosmic-ray knee. The
neutrino multiplicity employed in this calculation wasderived from a modiﬁed Elbert formula [30,31]. At PeV
energies and above, ‘‘prompt’’ atmospheric neutrinos fromdecays of charmed mesons are expected to dominate overthe conventional atmospheric neutrinos. We consider thedefault value of the prompt neutrino ﬂux from Enberg et al.
[32] modiﬁed to incorporate the cosmic-ray spectrum
model in Ref. [29].
In order to efﬁciently simulate high energy events withenergies exceeding 100 TeV at IceCube depths, the JULIeTpackage was used in which the propagation of neutrinos
was efﬁciently obtained by solving numerical transport
equations as described in Ref. [8].
Figure 2 shows examples of simulated signal and background events observed in the IceCube detector. The sizes
and colors of the spheres indicate the number and thetiming of photoelectrons (p.e.) observed in each DOM. A
signal muon event produces a number of stochastic energy
losses along the path. Tau events with energies greater than
10 PeV resemble muon tracks, except that they exhibit lessenergy loss due to their heavier masses. They may also
generate characteristic ‘‘double bang events’’ at energies
between 1 and 10 PeV due to neutrino interactions andsuccessive tau decays inside the detector volume. Particle
showers are induced by neutral current interactions ofneutrinos of any ﬂavor or by charged current interactions

FIG. 2 (color online). Event displays of simulated events. Eachsphere represents a DOM. Colors indicate the arrival time of thephoton (red indicates the earliest and blue the latest). The size ofthe sphere and the length of the horizontal lines at the rightborder indicate the measured amount of photoelectrons in each
DOM. Upper left: An upgoing muon entering into the detector
array with energy of 20 PeV induced by a neutrino of 500 PeV.
Upper right: A 300 PeV e induced cascade event. Lower panel:
A typical background atmospheric muon bundle event in thecurrent analysis induced by primary cosmic-ray energy of 1 EeV.

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PHYSICAL REVIEW D 88, 112008 (2013)

350

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300

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250
200

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5
100

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log10 NPE

The energy spectrum of atmospheric muons and neutrinos falls steeply with energy. The cosmogenic neutrino
ﬂuxes with their harder spectra are expected to dominate
over this background at high energies. Because the amountof deposited energy, i.e. the observable energy, is correlated with the energy of the incoming particles, the signal
events stand out against the background events at highenergy. Therefore, this analysis is targeted towards theselection of these high energy events.
The initial event ﬁlter selects events containing morethan 1,000 p.e. This ﬁltering eliminates a large number oflow energy atmospheric muon-induced events, typicallywith less than a few TeV energy. The ﬁltering process isperformed at the South Pole and the resulting EHE sample
is sent to the data warehouse at the northern hemisphere via
satellite. The samples contained a total of 4:0  107 and
6:0  107 events for IC79 and IC86, respectively.
The EHE sample transferred to the northern hemisphereis subjected to off-line hit cleaning in order to remove
coincident atmospheric muons and PMT noise. A hit represents a reconstructed pulse of photons from a waveformrecorded by a DOM and is characterized by its time andcharge. The initial hit cleaning is a time window cut on thehits outside the time interval between 4:4 and þ6:4 srelative to the time of the ﬁrst hit on the DOM with thehighest charge. Then a secondary hit cleaning based on
distances and hit time intervals between DOMs is applied.
Hits from the DeepCore strings are discarded at this stage
and not used for higher selection levels to keep the DOM
separation uniform across the detector volume. After these
hit cleanings, the analysis level sample is selected byrequesting at least 300 hits and 3200 p.e. in the wholedetector except DeepCore. This sample contains a total of
4:5  105 and 5:9  105 observed events for IC79 andIC86, respectively. The distribution of the total numberof p.e.’s (NPEs) versus the true energy of the incoming
particle for IC86 simulations of neutrino-induced muonsand cascades is shown in Fig. 3. The energies are sampledwhen the incoming particle is at 880 m from the IceCube
center. A clear correlation between NPE and the energy ofthe muons is observed. By selecting events with a NPE
above an appropriate threshold, low energy events dominated by atmospheric backgrounds are ﬁltered out. The
correlation also holds for cascade events although uncontained events with vertex positions outside the instrumentation volume weaken the correlation thereby reducing theselection efﬁciency for this type of event.

10

IV. EVENT SELECTIONS

The left panels in Fig. 4 show the NPE distributions atanalysis level for data and simulations for IC79 and IC86,
respectively. The signal cosmogenic neutrino distributions
dominate over the atmospheric  and  background
distributions in the high NPE region. Three cosmogenic
neutrino models are shown in the ﬁgure: Yoshida andTeshima [6] for an UHECR source distribution in theform of ð1 þ zÞm with the evolution parameter m ¼ 4
and the maximum redshift of the UHECR source distribution zmax ¼ 4, Ahlers et al. [33] (the best ﬁt model withm ¼ 4:6 and zmax ¼ 2:0), and Kotera et al. [17] [FanaroffRiley type II (FR-II)]. Atmospheric muon bundles are thedominant contribution at this level. Due to the yet unknown
chemical composition of UHECRs, the background rates
are estimated by the extreme assumptions of pure proton
and iron. The pure iron is employed in this analysis as ourbaseline model for the atmospheric muons since it yields
more muons compared to the pure proton case and hence
gives us a conservative background estimate. For the pureiron case the predicted rate is about a factor of 2 higher
than the rate observed in IceCube. The data are bracketedby the two compositions as shown in Fig. 4 by the shaded
area, demonstrating a reasonable agreement between theexperimental data and the atmospheric muon backgroundsimulations.
The directional information is also used to further discriminate signal from background. Since the backgroundof atmospheric muons is overwhelmingly large comparedto our signals above the horizon, a robust directional
reconstruction is crucial for the discrimination. For thispurpose, a track hypothesis is assumed to reconstruct atmospheric muons. We utilize different zenith angle reconstruction algorithms for IC79 and IC86. A so-called single
photoelectron (SPE) log-likelihood (LLH) ﬁtting based ona track hypothesis using the probability distribution of thearrival time of the ﬁrst photon in each DOM [34] islog NPEof electron neutrinos. These events called cascade events
generate spherical hit patterns in the detector. A background muon bundle event in the current study typicallycontains about 100 to 1000 muons with lateral separationsof about 10 m which results in a smoother energy loss
proﬁle compared to one from a single muon or tau event.

0

FIG. 3 (color online). Distributions of NPE versus the energies
of neutrino-induced muons (left) and neutrinos which induce
cascades (right) obtained at the analysis level with the IC86
signal Monte Carlo simulations. For illustrative purposes, an E1energy spectrum of the particles is assumed in these plots. The
muon and neutrino energies are given when the particle enters aradius of 880 m around the IceCube center. Cascade events
include all ﬂavor neutral current and e charged current interactions.

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M. G. AARTSEN et al.
IC79 data
background sum
atm. μ (single, iron)atm. μ (single, proton)atm. μ (coincident)
atm. ν conventional
atm. ν prompt
GZK ν Yoshida et al.
GZK ν Ahlers et al.
GZK ν Kotera et al.

105

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102
10

10-5
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cos θ

7.5

IC86 data
background sum
atm. μ (single, iron)atm. μ (single, proton)atm. μ (coincident)
atm. ν conventional
atm. ν prompt
GZK ν Yoshida et al.
GZK ν Ahlers et al.
GZK ν Kotera et al.

105
10

6.5

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10-2

10 6
10 5
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10 2
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1

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10

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IC86 data
background sum
atm. μ (single, iron)atm. μ (single, proton)atm. μ (coincident)
atm. ν conventional
atm. ν prompt
GZK ν Yoshida et al.
GZK ν Ahlers et al.
GZK ν Kotera et al.

10-1

10-3

10-5
3.5

IC79 data
background sum
atm. μ (single, iron)atm. μ (single, proton)atm. μ (coincident)
atm. ν conventional
atm. ν prompt
GZK ν Yoshida et al.
GZK ν Ahlers et al.
GZK ν Kotera et al.

10-1

10-3

Number of events

Number of events

104

Number of events

PHYSICAL REVIEW D 88, 112008 (2013)
106

Number of events

106

10-5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cos θ

FIG. 4 (color online). Distributions of NPE (left panels) andreconstructed zenith angle (right panels) are shown for theexperimental test samples of IC79 (upper panels) and IC86
(lower panels). The data are compared with expected background contributions from atmospheric muons and neutrinos,and signals from various cosmogenic (GZK) neutrino models[6,17,33]. The event numbers presented here are for the live
times of the test samples of the experimental data, 33.4 days forIC79 and 20.8 days for IC86. The signal distributions are the sumof all three neutrino ﬂavors. The background sum includes all
atmospheric muons and neutrinos. The single atmosphericmuons (pure iron) dominate the background so that the line isnearly identical to the line for the background sum. See text for
more detail.

performed for the IC79 sample. Then a cut on the reduced
log-likelihood (rLLH) parameter is applied to ensure goodﬁt quality. The parameter rLLH is the log-likelihood valueof the reconstructed track divided by the number of degrees
of freedom of the ﬁt. This rLLH cut removes coincident
atmospheric muons. For the IC86 sample, photon hits thathave a signiﬁcantly different timing compared to the one
from the main bulk of photon signals are masked using therobust regression technique [35]. Then the particle directions are reconstructed by applying the LineFit algorithm[11] to the remaining unmasked hits. The LineFit algorithm is based on a track hypothesis and uses a simple~ 2 , whereminimization of 2 ¼ i NPEi ðr~i  r~COG  ti vÞ
ti and NPEi represent the time of the ﬁrst photoelectron
and the number of photoelectrons recorded by the ith
DOM at the position r~i , respectively. The quantity r~COG i xi i NPEi yi i NPEi ziði NPE; i NPEi ; i NPEi Þ is the position of the NPEi NPEi
weighted center of gravity of the hits. The ﬁt ignores thegeometry of the Cherenkov cone and the optical propertiesof the medium and assumes light traveling with a velocity
v~ along a one-dimensional path through the detector, passing through the center of gravity. The inclusion of therobust regression technique signiﬁcantly improves the performance of the LineFit used in the previous study [9],allowing for simpler background rejection. The zenith
angle resolution of SPE LLH for background muon events
is about 0.5 for the IC79 EHE analysis level sample. The
zenith angle resolution from the LineFit with the robust
regression for background muons for the IC86 analysis
level sample is about 1 . These performances are sufﬁcient
to remove atmospheric muon bundle background events inthe current analysis.
The performance of the reconstruction on the signal
neutrinos highly depends on the shape of the events(Fig. 2). Since most of the signal neutrino events(> 80%) are expected to be muon or tau tracks, the reconstruction of zenith angles based upon track hypotheses as
described above gives sufﬁciently good signal selection
efﬁciency. The reconstructed directions of neutrinoinduced cascades, however, are only poorly correlatedwith the true neutrino direction and exhibit systematic
directional shifts. The SPE LLH reconstruction tends toshift the zenith angles towards the vertical while the
LineFit shifts them to the horizontal. The behavior of theshifts also changes when their vertex positions are close toor outside the boundary of the instrumentation volume. The
resulting systematic uncertainty is discussed in Sec. V.
The right panels in Fig. 4 show the event distributions atanalysis level as a function of the cosine of the reconstructed zenith angle. These distributions are compared tothe background and signal simulations. Atmospheric muon
bundles dominate in the downward-going region and atmospheric neutrinos dominate in the upward-going region.
The signal selection criteria were optimized based on
simulations of background and signal after the simulation
was veriﬁed using the test sample. A cosmogenic neutrino
model [6] (with m ¼ 4 and zmax ¼ 4) is used for the
optimization. The selection criteria do not severely dependon the particular choice of the cosmogenic model since theexpected energy spectrum is similar. Selection criteria are
obtained by optimizing the NPE threshold values in the
IC79 and IC86 samples separately such that the model
discovery factor [9,36] is minimized in each sample.
Figure 5 presents the event distributions in the plane of
NPE versus the cosine of the reconstructed zenith angle(cos ) for the test sample and simulations. The distributionsof the signal simulation are the sum of all three neutrino
ﬂavors. The solid lines in Fig. 5 indicate the ﬁnal selection
criteria for each sample. The events above the lines are
considered to be signal event candidates. The essential pointof this analysis is to select high NPE events against backgrounds regardless of the event shape. A zenith-angledependent high NPE threshold is required to eliminate the112008-6

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PROBING THE ORIGIN OF COSMIC RAYS WITH . . .

-3

10

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Atm. μ (IC86)

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Cosmogenic ν (IC86)

6.5

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Cosmogenic ν (IC79)

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Obs. test data (IC86)
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log NPE

Atm. μ (IC79)

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7

PHYSICAL REVIEW D 88, 112008 (2013)
10

10

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log NPE10log NPE

7.5

3.5

10

-1 -0.8 -0.6 -0.4 -0.2 0

0.2 0.4 0.6 0.8

cos θ

1

10-6

FIG. 5 (color online). Event number distributions on the plane of NPE and cosine of reconstructed zenith angle (cos ) for the IC79
run (upper panels) and the IC86 run (lower panels). The experimental test samples are shown in left panels. The backgroundsimulations of atmospheric muon (middle-left panels), and the conventional atmospheric neutrino and prompt atmospheric neutrino[32] (middle-right panels), and simulation of signal cosmogenic neutrino model [6] (right panels) are also shown. The colors indicate
event numbers per live time of 33.4 days and 20.8 days for the IC79 and IC86 test samples, respectively. The signal distributions are thesum of all three neutrino ﬂavors. The solid lines in each panel indicate the ﬁnal selection criteria.

atmospheric muon background for the downward-goingregion, while a constant threshold value is placed in thezenith region of cos  & 0:1, where no atmospheric muon
background is expected. The predicted number of signal andbackground events passing the ﬁnal selection criteria arepresented in Table I along with the observed number of
events in the two experimental samples.
The effective neutrino detection areas at ﬁnal selection
criteria for the different IceCube detector conﬁgurations
are shown in Fig. 6. The effective areas are given for eachneutrino ﬂavor, averaged over 4 solid angle for IC79 andIC86. The areas are averaged over equal ﬂuxes of neutrinos
and antineutrinos. Below 5 PeV, the effective area forelectron neutrinos exceeds that of muon or tau neutrinos.
For particle cascades induced by charged current

interactions of electron neutrinos, their energies are deposited completely inside the detector if their interaction
vertex lies sufﬁciently inside the instrumented volume.
Contrarily muons (taus) from muon (tau) neutrino interactions only partially deposit their energies in the detector
volume. Therefore, even though tracks have a longer pathin the detector, they satisfy the NPE criteria less frequently(Fig. 5). At higher energies the effective area for tracks islarger because they can be generated in an increasingly
larger volume and still reach the detector. Above 100 PeV
cascades contribute less than 20% to the observable eventsfrom cosmogenic neutrino ﬂuxes. The right panel in Fig. 6
shows the effective area summed over all three neutrino
ﬂavors for IC79 and IC86 together with that for IC40
from the previous analysis [9]. The current analysis has

TABLE I. Number of events passing cuts at on-line ﬁltering, off-line analysis, and ﬁnal level with 285.8 days of effective live timefor IC79 and 330.1 days for IC86 (excluding test sample data). One cosmogenic neutrino model [6] (with m ¼ 4 and zmax ¼ 4) istaken to evaluate the benchmark signal rates. The background rates include atmospheric muons assuming a pure iron primary
composition, conventional atmospheric neutrinos, and prompt atmospheric neutrinos. Analysis sample requests the number of hit
DOMs  300, log 10 ðNPEÞ  3:5 for IC79 and IC86, and an additional requirement of rLLH < 8 for IC79. Systematic uncertainties inthe expected event rates at the ﬁnal selection level are given as asymmetric error intervals after the statistical errors.
Experimental
IC79
IC86

IC79

IC86

EHE ﬁlter level

4:0  107 6:0  107

4:4  107

8:9  107

2.1

2.4

Analysis level

4:5  105

5:9  105

8:5  105

1:3  106

1.5

1.8

0

2

Contributions samples

Final level

Background MCBenchmark signal MC [6]
IC79
IC86

þ0:119
þ0:015
þ0:142
0:056  0:002þ0:028
0:041 0:026  0:0030:017 0:876  0:0040:105 1:043  0:0060:134

112008-7

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PHYSICAL REVIEW D 88, 112008 (2013)
105

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IC79

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102

10

1

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5

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7

8

9

10

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IC40

102

10

1

5

log (Eν/GeV)

6

5

IC86

103

10-1

11

10

νe
νμ
ντ

Neutrino Effective Area [m2]

νe
νμ
ντ

Neutrino Effective Area [m2]Neutrino Effective Area [m2]

105

7

8

9

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11

104

IC79
IC86

10

3

102

10

1

10-1

5

6

7

10

8

9

10

11

log (Eν/GeV)

log (Eν/GeV)

10

10

FIG. 6 (color online). The IceCube neutrino effective area at ﬁnal selection criteria with different string conﬁgurations, IC79 (leftpanel) and IC86 (middle panel) for each neutrino ﬂavor, averaged over 4 solid angle. The areas are averaged over equal amounts ofneutrinos and antineutrinos. Three ﬂavor sums of the effective areas are shown in the right panel. The effective area from the previous
search [9] with 40 string conﬁguration of IceCube (IC40) is also shown for comparison. Exposure of the sample used in this analysis isobtained by multiplying the effective area with the effective live time without test samples (333.5 days, 285.8 days, and 330.1 days forIC40, IC79, and IC86 , respectively) and 4 solid angle. The sharp peaked structure at 6.3 PeV for electron neutrinos is due to the
Glashow resonance [37].

approximately a factor of 2 larger effective area compared
to IC40. The difference between the effective areas forIC79 and IC86 below 30 PeV originates from the different
NPE thresholds. The slight difference above 3  103 PeV
is due to the rLLH cut in IC79.

V. SYSTEMATIC UNCERTAINTIES
Table II summarizes the statistical and systematic errors
for signal, atmospheric muon and neutrino, prompt atmospheric neutrino, and the total background.

TABLE II. List of the statistical and systematic errors on the signal, atmospheric muon and neutrino, prompt neutrino, and the total
background rate. The uncertainties in the signal rate are estimated for the cosmogenic ﬂux of Yoshida and Teshima [6] for ðm; zmax Þ ¼
ð4; 4Þ. The uncertainties in the background rates are evaluated against the baseline estimation by CORSIKA-SIBYLL [25,26] with apure iron composition hypothesis for atmospheric muons and the Gaisser-H3a model [29] for atmospheric neutrinos. The uncertainties
in the prompt neutrino rate are estimated using the prediction by Ref. [32]. The systematic and statistical errors listed here are relative
to the event rates for each signal and background source.
Cosmogenic
 signal (%)

Atmosphericmuon (%)

Conventional
Atmospheric
neutrino (%)

Promptneutrino (%)

Totalbackground (%)

Statistical error

0:4

9:1

9:8

1:1

4:5

DOM efﬁciency

þ1:5
5:1

þ41:9
42:7

þ73:2
17:9

þ33:6
9:6

þ43:1
26:1

Ice properties/detector response

7:2

47:7

44:8

30:8

41:7

Neutrino cross section

9:0









Sources

Photonuclear interaction

þ10:0









LPM effect

1:0









Angular shift for cascades

0:5









Cosmic-ray ﬂux variation



þ30:0
50:0

30:0

30:0

þ18:7
26:3

Cosmic-ray composition



79:1





36:7

Hadronic interaction model



þ17:7





þ8:1

 yield from cosmic-ray nucleon





15:0



2:2

Prompt model uncertainty







þ31:6
40:4

þ12:6
16:1

Total

0:4ðstatÞ

9:1ðstatÞ

9:8ðstatÞ

1:1ðstatÞ

4:5ðstatÞ

þ13:6
12:4 ðsystÞ

þ54:5
100 ðsystÞ

þ80:5
58:7 ðsystÞ

þ55:0
59:8 ðsystÞ

þ49:3
68:7 ðsystÞ

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PHYSICAL REVIEW D 88, 112008 (2013)

the one used in this analysis [44] at 10 EeV, the peakenergy of primary cosmic rays that produce atmosphericmuon events passing the ﬁnal selection criteria. The contribution of the cosmic-ray normalization to the uncertainty
in the atmospheric neutrino rate is estimated in a similar
way at energies from 1 to 100 PeV from various models[29,45]. In addition, a systematic uncertainty for the atmospheric neutrino rate arises from the uncertainty of theparametrization of the neutrino multiplicity as described inSec. III. A comparison to the full simulation by CORSIKA[25] provides the relevant uncertainty. The systematic uncertainties for backgrounds associated with the photon
detection efﬁciency and the optical properties of the ice
are determined in the same manner as for signal events.
The atmospheric neutrino background is calculated over4 solid angle and simulated independently of the atmospheric muon background. In reality, downward-going
atmospheric neutrino events would be accompanied byatmospheric muons, which improve their geometrical reconstruction. Because correctly reconstructed downwardgoing events are mostly rejected due to the higher NPE
threshold employed in the ﬁnal event selection, the background rate obtained from the independent neutrino andmuon simulations is likely overestimated.
The systematic error on the prompt neutrino ﬂux isestimated similarly. A relatively large uncertainty arises
from the parametrization in the framework of the Enberg
et al. model [32] which we used for the calculation of thebaseline rate of prompt neutrinos. A possible nonperturbative QCD contribution in charm production involves an evenlarger uncertainty. We have not observed clear evidence forprompt contributions in atmospheric neutrinos so far [46].
80
70
60

[p.e. / ns]

One of the dominant sources of systematic uncertainties inthe signal event rates is the error associated with theCherenkov photon measurement, namely the relationshipbetween measured NPE and the energy of the charged
particles. This is due to limitations in the understanding ofdetector sensitivities, photon propagation in the ice, and thedetector response to bright events which, for example, involves saturation effects of the DOMs. This uncertainty is
estimated by calibrating the absolute sensitivity of the DOMs
in the laboratory and by measuring it in situ using a lightsource codeployed with the DOMs in the ice [9,11]. The
other uncertainties in the signal rates involve the relevantinteractions of neutrinos and leptons produced during the
propagation through the Earth. For example, the LandauPomeranchuk-Migdal (LPM) effect [38,39] can be importantsince it elongates electromagnetic showers. The elongatedshower length is about 20–40 m for 1–10 EeV electrons [40],thus still being comparable to the IceCube DOM separationof 17 m, and hence negligible. Uncertainties due to otherpropagation effects are estimated as described in [11].
The uncertainty of the systematic shifts of reconstructed
zenith angles for cascade events causes a systematic error
in the estimation of the signal neutrino passing rate.
The effect is NPE dependent and thus energy dependent.
We artiﬁcially vary the systematic zenith angle shift bydifferent factors to evaluate the resulting uncertainties. The
complete randomization of zenith angles was found tobring the largest reduction of the cascade event selection
efﬁciency. The reduction is 20.0% for events with energies
below 10 PeV, 8.5% between 10 and 100 PeV, and 2.0%
above 100 PeV. Since most of the cosmogenic neutrinosignal (99.6%) is expected above 10 PeV and the present
analysis is mostly sensitive to track events above 10 PeV as
seen in Fig. 6, the effect on the cosmogenic neutrino signal
rate is quite limited. The systematic error on the overallsignal rate due to the limited performance of the cascade
event reconstruction is estimated to be 0:5%.
Systematic errors in the atmospheric muon backgroundrate arise from uncertainties in the primary cosmic-ray
composition, the hadronic interaction model implemented
in the air shower simulation, and the cosmic-ray ﬂux
variation at the relevant energies. The two extreme casesof the cosmic-ray compositions, pure iron and pure proton,
are used. In the current analysis, the iron-only hypothesis isused for the baseline background rates. This leads to ahigher, i.e. conservative, estimate of the photon yield fromthe muon bundles induced by primary cosmic-ray particles
at a particular energy. The difference between the pure-ironand the pure-proton hypothesis then provides the size ofthe relevant systematic uncertainty. The uncertainty associated with the hadronic interaction model is estimated byswitching the model from SIBYLL 2.1 [26] to QGSJET-II03 [41] in the simulations. The uncertainty in the cosmicray ﬂux normalization is estimated from the variance in theﬂux measured by several experiments [42,43] relative to

50
40
30
20
10
0
0

50

100

150

200

250

300

350

400

time [ns]FIG. 7. Waveforms of PMT outputs captured by three DOMs
in the neighborhood of the reconstructed vertex position of theevent obtained in January, 2012. The waveform drawn as a solid
curve is recorded in the DOM closest to the vertex (the brightest
DOM). The waveform in the lower (upper) next to nearest to thebrightest DOM on the same string is shown as a dashed (dotted)
curve. Photons arrive earlier in the upper DOM because it iscloser to the cascade vertex than the lower DOM. The signals
from the upper DOM exhibit clear signatures of scattered late
photons, suggesting that this cascade is a downward-going event.

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PHYSICAL REVIEW D 88, 112008 (2013)

VI. RESULTS
Two events passing the ﬁnal selection criteria areobserved [20]. The waveform proﬁles and the detector hit
patterns of both events are consistent with that of
Cherenkov photons from particle cascades induced byneutrinos well inside the IceCube instrumentation volume.
There is no indication of outgoing/incoming muon or tau
tracks. Several waveforms captured by the DOMs in theneighborhood of one of the reconstructed cascade vertex
position are shown in Fig. 7. The total charge contained in
the waveforms plays a dominant role in estimating thedeposited energy of the cascade. The leading edge time
mainly determines the vertex position. The relative widthsof the waveforms in DOMs in the forward and rear directions of the cascade are relevant for the reconstruction of
the arrival direction of neutrinos. Since photons can only
reach the backward direction by scattering, the distributionof photon arrival times is much wider in the backward
region of the cascades. The relations of the waveformfeatures to the energy, direction, and vertex position are
described using a single likelihood function built from a
product of Poisson probabilities of the number of photons
predicted to arrive in a given time bin against the number
extracted from the recorded waveform. Minimizing the
log-likelihood under simultaneous variation of the energy
and geometry of the cascade hypothesis yields estimates ofthe deposited energy, direction, and interaction vertex of
the cascade.
The reconstructed deposited energies of the two
observed cascades are 1:04  0:16 PeV and 1:14 
0:17 PeV, respectively. The statistical energy resolutions
for these events are obtained by simulating cascades withparameters close to the reconstructed energies and cascadevertices, and are found to be 3%. The total error on theenergy is dominated by systematic uncertainties. These
include the absolute detection efﬁciency of the DOM andthe optical properties of the ice, both of which are major
factors when relating the number of observed photons tothe cascade energy. The size of the errors is estimated byreconstructing simulated events with various models of theice properties.
The incoming neutrino energy corresponds exactly tothe deposited cascade energy if a charged current interaction of an electron neutrino induces a cascade. For neutral
current reactions of neutrinos of any ﬂavor, only a fractionof the neutrino energy is transferred to a cascade dependingon the inelasticity of the collision. Because the present
analysis is incapable of distinguishing between neutrino
ﬂavors, both interaction channels are included when constructing the probability density function (PDF) of theenergy of the incoming neutrino. Here, the systematic
uncertainties for the deposited energies are taken into
account. The PDF of the neutrino energy at the surfaceof the Earth is built by simulating neutrino interactions
over a wide energy range each time evaluating theTABLE III. The 90% C.L. of the energy range of the primary
neutrino in PeV at the Earth’s surface for the two events for anenergy spectrum following an E2 power law.
Energy range (90% C.L.)
Event (August, 2011)
Event (January, 2012)probability that the resulting cascade energy matches theestimated energy and its uncertainty. The 90% C.L. energy
ranges obtained from the PDFs for neutrino spectra with anE2 power law ﬂux are summarized in Table III. The ﬂavor
ratio is assumed to be e : : ¼ 1:1:1. Since theneutrino-nucleon interaction cross section increases withneutrino energy, the possibility that the energy of the
primary neutrino is much higher than the observed cascadeenergy is not entirely negligible, depending on the neutrino
spectrum. For example, the 90% C.L. energy range for acosmogenic neutrino model [33] extends to about 500 PeV,
which shows that the energy range heavily depends on the
shape of the energy spectrum.
VII. TESTS ON COSMOGENICNEUTRINO MODELS
Our results are characterized by two observational facts:
the detection of two neutrinos with deposited energies ofabout 1 PeV and the nondetection of neutrinos with higher
deposited energies. First, we investigate whether a single
cosmogenic neutrino model can account for these two
observational facts simultaneously. Second, we constrain
the UHECR origin with the present results. Because most
cosmogenic neutrinos have energies above 100 PeV, tests
on the event rate above this energy expected from cosmogenic neutrino models under various assumptions on the
UHECR spectrum and the evolutions of the source distributions will lead to constraints on the UHECR origin. We
note that the energy threshold of 100 PeV is an a posteriori
parameter and, hence, the results are not part of the blind
analysis.
The statistical signiﬁcance of these tests is limited by ourobservational exposure. To obtain the best constraints, we
combine the exposure of the previously published results
obtained by the half-completed IceCube detector with its
40 string conﬁguration (IC40) [9] with the present results
hereafter. The IC40 data increase the observational exposure by about 30%, depending on the neutrino energy, as
displayed in Fig. 6.
A. The full energy range test
We introduce here an energy inclusive test which checks
the consistency of the energy distributions of cosmogenic
neutrino models with the observed two events. A p value iscalculated with the Kolmogorov-Smirnov test (KS test)
using the energy spectrum of the neutrino models and the112008-10

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TABLE IV. P values PE in Eq. (1) are listed for several
neutrino models. All the models shown here assume thecosmic-ray primaries to be protons and different spectral
indices/cutoff energies at sources, IR/UV backgrounds, as well
as different cosmological evolution parameters and extension inredshift for the sources. P values for E2 spectra with various
cutoff energies are also shown for reference.
 ModelRMRF ¼

P value

Yoshida and Teshima [6]m ¼ 4:0, zmax ¼ 4:0
Ahlers et al. [33]m ¼ 4:6, zmax ¼ 2:0 (‘‘the best ﬁt’’)Kotera et al. [17]GRB
Kotera et al. [17]Fanaroff-Riley type II
E2With cutoff at 10 PeV
With cutoff at 100 PeV
With cutoff at 1 EeV

0.077
0.075
0.052
0.039
0.18
0.13
0.11

energy PDFs of the two observed events. The expectedenergy distributions from the neutrino models are obtainedby multiplication of the neutrino effective area with thepredicted neutrino energy spectrum. This allows us toanalytically calculate p values without relying on extensiveMonte Carlo simulations. In order to evaluate the ﬁnal
p value, PE , that the two events (energies E1 and E2 ) areconsistent with a cosmogenic ﬂux model, the p value
obtained in the KS test PKS ðE1 ; E2 Þ is convoluted withthe energy PDFs of the two events as follows:PE ¼

B. The ex post facto test above 100 PeV
Here, a prospective event rate in the energy region above
100 PeV is compared to the observational upper limit. A
constraint on a given neutrino model is set by calculating
the model rejection factor (MRF) [48] given byZ

dE1 1 ðE1 ÞZ

dE2 2 ðE2 ÞPKS ðE1 ; E2 Þ;(1)where i is the energy PDF of the ith event. Note that the
PDF is different for each model to be tested as described in
the previous section. Table IV summarizes the resulting
p values of this test: all cosmogenic neutrino models areinconsistent with the two observed events at more than
90% C.L.
The recent follow-up analysis [47] revealed the existence of neutrinos at TeV energies above the atmosphericbackground, in addition to the two PeV events reported
in Ref. [20]. The event distribution indicated either asubstantially softer spectrum than E2 or the presence ofa break or cutoff at PeV energies, although the statistics arelimited. The present analysis conﬁrmed this picture using
the KS test with an E2 spectrum hypothesis as Table IVlists the resultant p values with various assumptions of thespectral cutoff energies. The observed PeV events areunlikely to originate from a bulk of neutrinos with energies
extending well above PeV, regardless of the characteristicsof the events at TeV energies found in the follow-up
analysis.

N100ð1 Þ%
;


(2)

where N100ð1 Þ% is the upper limit of number of events at
100ð1  Þ% C.L. and  is the event rate of signal
neutrino events predicted by the model above 100 PeV.
Any model with RMRF 1 is rejected at  100ð1  Þ%
C.L. in this approach. For ¼ 0:1, N90% ¼ 2:27 in the
Feldman-Cousins approach [49] for a null observation witha conventional background of a 0.16 event. The large
number of background events comes mainly from theIC40 analysis contributing a 0.11 event [9]. Although theprobability that the original neutrino energy of the two
observed events is higher than 100 PeV is expected to besmall, this is taken into account by calculating the mostprobable upper limit:
N100ð1 Þ% ¼

2
XnPn N100ð1
Þ% :

(3)

n¼0

Here, Pn is the probability of ﬁnding n events above
100 PeV determined by the energy PDFs of the two events,nand N100ð1
Þ% is the upper limit for n observed events.
Since the energy PDF highly depends on the shape of theenergy spectrum, an appropriate shape of an energy spectrum has to be chosen. Since the two observed events were
found to be inconsistent with cosmogenic neutrino models
as shown in the previous subsection, the cosmogenic neutrino models are not used for the energy PDF, instead anE2 power law spectrum is used. The N90% is calculated
for the standard cosmogenic models and found to be 2.273,
which is slightly larger than for the case of a null detection.
The systematic uncertainty on the background estimates isincorporated using a method outlined in [50]. The p value
for a given model is obtained by requesting RMRF ¼ 1 in
Eq. (2).
Table V summarizes the p values for several neutrino
models. The maximal ﬂux allowed by the constraints fromthe diffuse photon ﬂux (labeled as ‘‘the maximal ﬂux’’ inthe table) is excluded at 95% C.L. It demonstrates that thepresent constraints from the limit on the ultrahigh energy
neutrino ﬂux are compatible with those from photon ﬂux
measurements by Fermi in the 10 GeV region [53].
In order to set constraints on characteristics of the
UHECR sources in a more comprehensive manner, a parametrization often used in the literature [6] is employed,in which the spectral emission rate per comoving volume
scales as ð1 þ zÞm for z zmax . The event rate at energies
above 100 PeV is calculated for a given m, and zmax using
the formula in Ref. [4]. The constraints on the parameter

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PHYSICAL REVIEW D 88, 112008 (2013)
5

TABLE V. Expected numbers of events from several neutrino
models and the p values for consistency with the present
observation in energy range above 100 PeV.
Event rate above 100 PeV P value

1.5

0.22

1.5

0.22

3.1

0.044

0.48

0.66

0.46

0.67

2.9

0.052

16

0:00203.9

0.021

space of m and zmax are derived by using Eq. (2), and are
displayed in Fig. 8.
C. Discussion
The models listed in the top two rows of Table IVassume
that the ankle structure which appears at 3 to 10 EeV in the
UHECR spectrum is due to the transition from the galactic
to the extragalactic component [54]. In this scenario, thecosmogenic neutrino generation mechanism is dominatedby collisions of UHECRs with the CMB photons which
results in a neutrino energy spectrum with a peak at about
1 EeV, well above the main regime of the energy range ofthe two observed events. This is the reason why thesemodels are inconsistent with the two observed events asshown in Table IV. The models in the lower two rows ofTable IV (Kotera et al. [17]) assume the ‘‘dip’’ transition
model [55] where the ankle structure is mainly caused bypair-production energy losses of UHECRs on diffuse infrared, optical, and ultraviolet backgrounds (IR/UV backgrounds) during intergalactic propagation. The neutrino
models in Kotera et al. use the IR/UV backgrounds asmodeled by Stecker et al. [56] which comprises an increased far-infrared bump at large redshift (note that the
IR/UV model employed in these neutrino models is now
disfavored by gamma-ray observation with Fermi-LAT[57]). Compared to the standard cosmogenic models, thedip and the IR/UV backgrounds leads to an increased
ﬂux of neutrinos at PeV energies, so that these models in

3

2

2

3

4

5

m

FIG. 8 (color online). Constraints on the UHECR source evolution parameters of m and zmax with the present analysis. The
semianalytic formulation [4] estimates the neutrino ﬂux for
calculating the limit shown here. The area above the solid lines
is excluded at the quoted conﬁdence level.

Kotera et al. could be more consistent with the observation.
However, even in these models, the collision of UHECRs
with CMB photons produces a bulk of neutrinos withenergies much higher than 100 PeV which should havebeen detected because of the signiﬁcantly larger effective
area at these energies. In addition, the substantial ﬂux at
PeV energies yields energy PDFs for the observed two
events very similar to those from an E2 spectrum. Since
the energy range for the E2spectrum
PDF
does not extend

to 10 PeV as shown in Table III, neutrinos with energy of
100 PeV or greater are less likely to be responsible for theobserved PeV cascades. Because of these reasons, p values
for these scenarios in Kotera et al. are small as shown in
Table IV. In conclusion, none of the cosmogenic scenarios
is consistent with the observation of the two events. This
indicates that models which predict neutrino spectra extending to energies well beyond 100 PeV will not explain
our measurements.
The model test based on the event rates above 100 PeV
indicates that strong source evolution models (m4) arenot responsible for the bulk of UHECRs. Among sources
categorized in this class are the FR-II radio galaxies, thelong-standing favorite as a candidate of the UHECR
emitters [58]. Similarly a strong source evolution modelfor gamma-ray bursts (GRBs) [59] is also rejected by ourobservation since the model produces higher neutrino ﬂux
than the FR-II model. The obtained limits are highly
complementary to the bound from the diffuse photon
ﬂux [53], because the cosmogenic neutrino intensity
around 1 EeV, the central energy range of the presented

112008-12

12

.
C.L

0.045

90%

3.1

4

C.L.

0.14

68%

2.0

z max

 ModelYoshida and Teshima [6]m ¼ 4:0, zmax ¼ 4:0
Kalashev et al. [51]m ¼ 5:0, zmax ¼ 3:0
Yoshida and Ishihara [4]m ¼ 5:0, zmax ¼ 2:0
Ahlers et al. [33]m ¼ 4:6, zmax ¼ 2:0(‘‘the best ﬁt’’)Ahlers et al. [33](‘‘the maximal ﬂux’’)
Kotera et al. [17]GRB
Kotera et al. [17]SFR
Kotera et al. [17]Fanaroff-Riley type II
Top-down 1 [52]SUSYTop-down 2 [52]GUTPROBING THE ORIGIN OF COSMIC RAYS WITH . . .

PHYSICAL REVIEW D 88, 112008 (2013)

ANITA-II(2010)

10-4
RICE(2012)-5

E2ν φ(Eν) [GeV cm-2 s-1 sr-1]

10

PAO(2012) ν τ limit x3

10-6
10-7

IceCube2012

10-8
Cosmogenic ν models
Engel et al.

10-9

Kotera et al. (FRII)
Ahlers et al. (max)

10-10

Ahlers et al. (best)
Yoshida et al.

10-11
6

8

10

log (Eν/GeV)
10

FIG. 9 (color online). All ﬂavor neutrino ﬂux differential
90% C.L. upper limit evaluated for each energy with a sliding
window of one energy decade from the present IceCube EHE
analysis including the IceCube exposure from the previously
published result (IC40) [9]. All the systematic errors are included. Various model predictions (assuming primary protons)
are shown for comparison; Engel et al. [7], Kotera et al. [17],Ahlers et al. [33], Yoshida and Teshima [6]. The modelindependent differential 90% C.L. upper limits for one energy
decade by other experiments are also shown for Auger (PAO)[62], RICE [63], ANITA [14,15] with appropriate normalization
by taking into account the energy bin width and the neutrino
ﬂavor. The upper limit for the  ﬂux obtained by Auger ismultiplied by 3 to convert it to an all ﬂavor neutrino ﬂux limit(assuming an equal neutrino ﬂavor ratio).

existence of two events in the ﬁnal sample. The 90% event
upper limit used in the calculation takes into account theenergy PDFs of each of the observed events using Eq. (3),where Pn is a function of the neutrino energy E andcorresponds to the probability of having n events in theinterval [log 10 ðE =GeVÞ  0:5, log 10 ðE =GeVÞ þ 0:5].
Here, the PDFs for an E2spectrum are used since
the two observed events are not consistent with a harder
spectrum such as from cosmogenic neutrino models. The
quasidifferential limit takes into account all the systematic
uncertainties described in Sec. V. The effect of the uncertainty due to the angular shift of the cascade events on theupper limit is negligible above 10 PeV (< 1%) as track
events dominate in this energy range. Below 10 PeV, theeffect weakens the upper limit by 17% because cascade
events dominate. Other systematic uncertainties are implemented as in previous EHE neutrino searches [9,11]. The
obtained upper limit is the strongest constraint in the EeV
regime so far. In the PeV region, the constraint is weakerdue to the detection of the two events. An upper limit for anE2 spectrum that takes into account the two observed
events was also derived and amounts to E2 e þ þ ¼
2:5  108 GeV cm2 s1 sr1 for an energy range of
1.6 PeV–3.5 EeV (90% event coverage).
IX. SUMMARY

search with IceCube, is stable against uncertainties in the
IR/UV backgrounds and the transition model between thegalactic and extragalactic component of the UHECRs[4,17,60,61]. We should note, however, that the obtainedbound is not valid if the mass composition of UHECRs is
not dominated by proton primaries. The dominance of
proton primaries is widely assumed in the models mentioned here while a dominance of heavier nuclei such asiron provides at least 2–3 times lower neutrino ﬂuxes. The
analysis is not sensitive enough to reach these ﬂuxes yet.

We analyzed the 2010–2012 data samples collected by
the 79- and 86-string IceCube detector searching for extremely high energy neutrinos with energies exceeding
1 PeV. We observed two neutrino-induced cascade events
passing the ﬁnal selection criteria. The energy proﬁles of
the two events indicate that these events are cascades withdeposited energies of about 1 PeV. The cosmogenic neutrino production is unlikely to be responsible for these
events. An upper limit on the neutrino rate in the energy
region above 100 PeV places constraints on the redshift
distribution of UHECR sources. For the ﬁrst time the observational constraints reach the ﬂux region predicted forsome UHECR source class candidates. The obtained upper
limit is signiﬁcantly stronger compared to our previous
publication [9] because of the enlarged instrumented volume and the reﬁned Monte Carlo simulations. Future dataobtained with the completed detector will further enhance
IceCube’s sensitivity to cosmogenic neutrino models.

VIII. THE MODEL-INDEPENDENT UPPER LIMITACKNOWLEDGMENTS

The quasidifferential, model-independent 90% C.L.
upper limit on all ﬂavor neutrino ﬂuxes e þ þ wasevaluated for each energy with a sliding window of one
energy decade. It is shown in Fig. 9 using the same method
as implemented in our previous EHE neutrino searches[9,11]. An equal ﬂavor ratio of e : : ¼ 1:1:1 is assumed here. A difference from the calculation of the limit
shown in our previous publications arises from theWe 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 Alumni 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

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PHYSICAL REVIEW D 88, 112008 (2013)

Scientiﬁc Computing Center, the Louisiana Optical
Network Initiative (LONI) grid computing resources;
Natural Sciences and Engineering Research Council of
Canada, WestGrid and Compute/Calcul 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 and Research (BMBF),
Deutsche Forschungsgemeinschaft (DFG), Helmholtz
Alliance for Astroparticle Physics (HAP), Research

Department of Plasmas with Complex Interactions(Bochum), Germany; Fund for Scientiﬁc Research(FNRS-FWO), FWO Odysseus Programme, Flanders
Institute to encourage scientiﬁc and technological researchin industry (IWT), Belgian Federal Science Policy Ofﬁce(Belspo); University of Oxford, United Kingdom; Marsden
Fund, New Zealand; Australian Research Council; Japan
Society for Promotion of Science (JSPS); the Swiss
National Science Foundation (SNSF), Switzerland;
National Research Foundation of Korea (NRF).

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PRL 111, 021103 (2013)

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PHYSICAL REVIEW LETTERSFirst Observation of PeV-Energy Neutrinos with IceCube
M. G. Aartsen,2 R. Abbasi,27 Y. Abdou,22 M. Ackermann,41 J. Adams,15 J. A. Aguilar,21 M. Ahlers,27 D. Altmann,9J. Auffenberg,27 X. Bai,31,* M. Baker,27 S. W. Barwick,23 V. Baum,28 R. Bay,7 J. J. Beatty,17,18 S. Bechet,12J. Becker Tjus,10 K.-H. Becker,40 M. Bell,38 M. L. Benabderrahmane,41 S. BenZvi,27 J. Berdermann,41 P. Berghaus,41
D. Berley,16 E. Bernardini,41 A. Bernhard,30 D. Bertrand,12 D. Z. Besson,25 G. Binder,8,7 D. Bindig,40 M. Bissok,1
E. Blaufuss,16 J. Blumenthal,1 D. J. Boersma,39 S. Bohaichuk,20 C. Bohm,34 D. Bose,13 S. Böser,11 O. Botner,39
L. Brayeur,13 H.-P. Bretz,41 A. M. Brown,15 R. Bruijn,24 J. Brunner,41 M. Carson,22 J. Casey,5 M. Casier,13 D. Chirkin,27
A. Christov,21 B. Christy,16 K. Clark,38 F. Clevermann,19 S. Coenders,1 S. Cohen,24 D. F. Cowen,38,37 A. H. Cruz Silva,41
M. Danninger,34 J. Daughhetee,5 J. C. Davis,17 C. De Clercq,13 S. De Ridder,22 P. Desiati,27 M. de With,9 T. DeYoung,38
J. C. Dı́az-Vélez,27 M. Dunkman,38 R. Eagan,38 B. Eberhardt,28 J. Eisch,27 R. W. Ellsworth,16 S. Euler,1 P. A. Evenson,31
O. Fadiran,27 A. R. Fazely,6 A. Fedynitch,10 J. Feintzeig,27 T. Feusels,22 K. Filimonov,7 C. Finley,34 T. Fischer-Wasels,40
S. Flis,34 A. Franckowiak,11 R. Franke,41 K. Frantzen,19 T. Fuchs,19 T. K. Gaisser,31 J. Gallagher,26 L. Gerhardt,8,7
L. Gladstone,27 T. Glüsenkamp,41 A. Goldschmidt,8 G. Golup,13 J. G. Gonzalez,31 J. A. Goodman,16 D. Góra,41 D. Grant,20
A. Groß,30 M. Gurtner,40 C. Ha,8,7 A. Haj Ismail,22 P. Hallen,1 A. Hallgren,39 F. Halzen,27 K. Hanson,12 D. Heereman,12
D. Heinen,1 K. Helbing,40 R. Hellauer,16 S. Hickford,15 G. C. Hill,2 K. D. Hoffman,16 R. Hoffmann,40 A. Homeier,11K. Hoshina,27 W. Huelsnitz,16,† P. O. Hulth,34 K. Hultqvist,34 S. Hussain,31 A. Ishihara,14,‡ E. Jacobi,41 J. Jacobsen,27
K. Jagielski,1 G. S. Japaridze,4 K. Jero,27 O. Jlelati,22 B. Kaminsky,41 A. Kappes,9 T. Karg,41 A. Karle,27 J. L. Kelley,27
J. Kiryluk,35 F. Kislat,41 J. Kläs,40 S. R. Klein,8,7 J.-H. Köhne,19 G. Kohnen,29 H. Kolanoski,9 L. Köpke,28 C. Kopper,27
S. Kopper,40 D. J. Koskinen,38 M. Kowalski,11 M. Krasberg,27 K. Krings,1 G. Kroll,28 J. Kunnen,13 N. Kurahashi,27
T. Kuwabara,31 M. Labare,13 H. Landsman,27 M. J. Larson,36 M. Lesiak-Bzdak,35 M. Leuermann,1 J. Leute,30
J. Lünemann,28 J. Madsen,33 R. Maruyama,27 K. Mase,14 H. S. Matis,8 F. McNally,27 K. Meagher,16 M. Merck,27
P. Mészáros,37,38 T. Meures,12 S. Miarecki,8,7 E. Middell,41 N. Milke,19 J. Miller,13 L. Mohrmann,41 T. Montaruli,21,§
R. Morse,27 R. Nahnhauer,41 U. Naumann,40 H. Niederhausen,35 S. C. Nowicki,20 D. R. Nygren,8 A. Obertacke,40
S. Odrowski,30 A. Olivas,16 M. Olivo,10 A. O’Murchadha,12 L. Paul,1 J. A. Pepper,36 C. Pérez de los Heros,39
C. Pfendner,17 D. Pieloth,19 E. Pinat,12 N. Pirk,41 J. Posselt,40 P. B. Price,7 G. T. Przybylski,8 L. Rädel,1 M. Rameez,21
K. Rawlins,3 P. Redl,16 R. Reimann,1 E. Resconi,30 W. Rhode,19 M. Ribordy,24 M. Richman,16 B. Riedel,27
J. P. Rodrigues,27 C. Rott,17,∥ T. Ruhe,19 B. Ruzybayev,31 D. Ryckbosch,22 S. M. Saba,10 T. Salameh,38 H.-G. Sander,28
M. Santander,27 S. Sarkar,32 K. Schatto,28 M. Scheel,1 F. Scheriau,19 T. Schmidt,16 M. Schmitz,19 S. Schoenen,1
S. Schöneberg,10 A. Schönwald,41 A. Schukraft,1 L. Schulte,11 O. Schulz,30 D. Seckel,31 Y. Sestayo,30 S. Seunarine,33
C. Sheremata,20 M. W. E. Smith,38 M. Soiron,1 D. Soldin,40 G. M. Spiczak,33 C. Spiering,41 M. Stamatikos,17,¶ T. Stanev,31
A. Stasik,11 T. Stezelberger,8 R. G. Stokstad,8 A. Stößl,41 E. A. Strahler,13 R. Ström,39 G. W. Sullivan,16 H. Taavola,39
I. Taboada,5 A. Tamburro,31 S. Ter-Antonyan,6 G. Tešić,38 S. Tilav,31 P. A. Toale,36 S. Toscano,27 M. Usner,11D. van der Drift,8,7 N. van Eijndhoven,13 A. Van Overloop,22 J. van Santen,27 M. Vehring,1 M. Voge,11 M. Vraeghe,22
C. Walck,34 T. Waldenmaier,9 M. Wallraff,1 R. Wasserman,38 Ch. Weaver,27 M. Wellons,27 C. Wendt,27
S. Westerhoff,27 N. Whitehorn,27 K. Wiebe,28 C. H. Wiebusch,1 D. R. Williams,36 H. Wissing,16 M. Wolf,34
T. R. Wood,20 K. Woschnagg,7 C. Xu,31 D. L. Xu,36 X. W. Xu,6 J. P. Yanez,41 G. Yodh,23 S. Yoshida,14P. Zarzhitsky,36 J. Ziemann,19 S. Zierke,1 A. Zilles,1 and M. Zoll34(IceCube Collaboration)
1
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
School of Chemistry and Physics, University of Adelaide, Adelaide South Australia 5005, Australia
3
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, Alaska 99508, USA
4
CTSPS, Clark-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 und Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
11
Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany
20031-9007=13=111(2)=021103(7)16021103-1

Ó 2013 American Physical Society

PRL 111, 021103 (2013)

PHYSICAL REVIEW LETTERS

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12

Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
13
Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
14Department of Physics, Chiba University, Chiba 263-8522, Japan
15
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
16
Department of Physics, University of Maryland, College Park, Maryland 20742, USA
17
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210, USA
18
Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA
19
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germany
20
Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1
21Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
22
Department of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
23
Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
24
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerland
25
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
26
Department of Astronomy, University of Wisconsin, Madison, Wisconsin 53706, USA
27
Department of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, Wisconsin 53706, USA
28
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
29
Université de Mons, 7000 Mons, Belgium
30Technical University of Munich, D-85748 Garching, Germany
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, United Kingdom
33
Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA
34
Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
35
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
36
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA37
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
38
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
39
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
40
Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
41
DESY, D-15735 Zeuthen, Germany(Received 19 April 2013; published 8 July 2013)
We report on the observation of two neutrino-induced events which have an estimated deposited energy
in the IceCube detector of 1:04  0:16 and 1:14  0:17 PeV, respectively, the highest neutrino energies
observed so far. These events are consistent with fully contained particle showers induced by neutralcurrent e;; ( e;; ) or charged-current e ( e ) interactions within the IceCube detector. The events werediscovered in a search for ultrahigh energy neutrinos using data corresponding to 615.9 days effective live
time. The expected number of atmospheric background is 0:082  0:004ðstatÞþ0:041
0:057 ðsystÞ. The probabilityof observing two or more candidate events under the atmospheric background-only hypothesis is
2:9  103 (2:8 ) taking into account the uncertainty on the expected number of background events.
These two events could be a ﬁrst indication of an astrophysical neutrino ﬂux; the moderate signiﬁcance,
however, does not permit a deﬁnitive conclusion at this time.
DOI: 10.1103/PhysRevLett.111.021103

PACS numbers: 95.85.Ry, 95.55.Vj, 98.70.Sa

Astrophysical neutrinos are key probes of the highenergy universe. Because of their unique properties,
neutrinos escape even dense regions, are undeﬂected ingalactic or extragalactic magnetic ﬁelds, and traverse thephoton-ﬁlled universe unhindered. Thus, neutrinos provide
direct information about the dynamics and interiors ofcosmological objects of the high redshift universe likegamma-ray bursts and active galactic nuclei. Neutrinos atenergies above several hundred TeV are particularly interesting as the atmospheric background in this region is very
low and a few astrophysical neutrinos can be signiﬁcant.
This Letter reports on the observation of two high-energy
particle shower events discovered in a search for ultrahighenergy neutrinos above about 1 PeV using the IceCube
detector.
IceCube [1] detects and reconstructs neutrinos byrecording Cherenkov photons emitted from secondary
charged particles produced in neutral-current (NC) or
charged-current (CC) interactions of the neutrinos in the2800 m thick glacial ice at the geographic South Pole.
IceCube was built between 2005 and 2010. It consists ofan array of 5160 optical sensors [digital optical modules,(DOMs)] on 86 strings at depths between 1450 and 2450 m
that instrument a volume of 1 km3 of ice. Eight of the 86
strings belong to the DeepCore subarray [2], a more
densely instrumented volume in the bottom center of the021103-217rejects downward-going atmospheric muons by employing
event reconstructions based on a track hypothesis in combination with a higher NPE selection criterion in the
downward-going region. All remaining events above the
combined NPE threshold are considered to be signal candidates independent of their topological properties.
Data were collected between May 2010 and May 2012,
an effective live time of 615.9 days excluding 54.2 days
used for the optimization of the analysis. From May 2010
to May 2011, DOMs on 79 strings (IC79) were operational(285.8 days live time with 33.4 days excluded). This period
was immediately followed by the ﬁrst year data taking withthe full 86-string (IC86) detector that lasted until May 2012
(330.1 days live time with 20.8 days excluded). The IC86
conﬁguration is shown in Fig. 1. Events are triggered wheneight or more DOMs record signals in local coincidences
which occur when a nearest or next-to-nearest DOM on thesame string triggers within 1 s [4].
The data are ﬁltered at the South Pole with a condition
NPE  1000, and then sent to a northern computer farm
via satellite. In order to avoid biases, we performed a blind
analysis and only 10% of the data were used to develop
the analysis. Photon arrival times are extracted from eachwaveform and stored as ‘‘hits.’’ To remove hits fromcoincident noise, a two-staged cleaning based on the spatial separation and the time interval between hits is applied.
Data from the DeepCore strings are discarded to maintain uniformity across the detector volume. To reject
downward-going atmospheric muon background, only
events with at least 300 hits and NPE  3200 are retained.
To further reduce this background, the directions of theremaining events are reconstructed with a track hypothesis,
and a stricter NPE criterion for downward-going tracks isapplied [see Fig. 2 and Eq. (1)]: for IC79, a log-likelihood
ﬁt is performed [6] and an event selection based on a ﬁt
quality parameter is applied to remove events which contain muons from independent air showers. For IC86, arobust regression technique [7,8] is utilized to remove
hits that have a timing signiﬁcantly different fromwhat is expected from the bulk of the photons from amuon track. Afterwards, the direction of the particle isFIG. 1 (color online). Surface view of the full IceCube detector layout. Filled marks represent the positions of the IceCube
strings. Red marks in the central region are the DeepCore strings.
Squares represent the strings that did not exist in the IC79
conﬁguration. Open circles are the positions of the closest strings
to the observed two cascade events. Stars are their reconstructedvertex positions.

detector. Each DOM consists of a 10’’ photomultiplier tube
[3] in a spherical glass pressure vessel. Events are recorded
as a series of pulses (waveform) in each DOM [4] where
two basic neutrino event signatures are distinguished: a
tracklike light pattern originating from neutrino-induced
muons (tracks) and a spherical light pattern produced byhadronic or electromagnetic particle showers (cascades).
The analysis selects neutrino candidates calorimetricallyusing the total number of observed photoelectrons ineach event (NPE) [4] as a proxy of the deposited energy[5], thus, retaining both bright tracks and cascades.
Backgrounds come from muons and neutrinos generated
in interactions of cosmic rays in the atmosphere. Becauseof their steeply falling energy spectra, little background is
expected in the signal region above 1 PeV. The zenith angle
distribution of atmospheric muons peaks in the downwardgoing direction and sharply decreases towards the horizon
with a cutoff at a zenith angle  of cos 0:15 due toabsorption in Earth. The atmospheric neutrino distributions
have a weaker zenith-angle dependence. The analysis

1

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log NPE

7.5

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PRL 111, 021103 (2013)

10-1

6
10-2
5.5
10-3
5
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10-5

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10-6

FIG. 2 (color online). Distribution of NPE and reconstructed zenith angle for (a) the IC79 experimental test sample, (b) the total
background, and (c) cosmogenic signal neutrino [11]. The colors show event numbers per live time of 33.4 days. The solid lines
represent the ﬁnal selection criteria for IC79.

021103-318

reconstructed with a basic algorithm that assumes a plane
wave of photons traveling along the direction of the muon,‘‘LineFit’’ [5]. Both algorithms reconstruct muon tracks
with a zenith angle resolution of 1 or better.
Cascade events which pass the initial hit and NPE
selection criteria are considered signal events and, therefore, should be affected as little as possible by the event
rejections just described. As they resemble pointlike lightsources, the reconstruction behavior of the two algorithms
is indeed quite different ﬁnding nearly arbitrary zenith
angles, albeit with a tendency toward upward-going andhorizontal directions for the log-likelihood ﬁt and LineFit,
respectively. Since, for these directions, the NPE thresholdvalue is lower than for downward-going events [see Fig. 2
and Eq. (1)], such events are retained in the ﬁnal sample
even if they would be rejected on account of their true
direction.
The NPE threshold values for the two samples wereseparately optimized based on the simulations to maximize
the signal [9,10] from the cosmogenic neutrino model [11].
Figure 2 shows the event distributions for the simulations
and the experimental IC79 test sample (a live time of 33.4
days). The solid lines in Fig. 2 represent the ﬁnal selection
criteria for IC79 where events above the lines constitute theﬁnal sample. The ﬁnal selection criteria for the IC86
sample arelog10 NPE 

8
>
< 4:8

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ
>: 4:8 þ 1:6 1 

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PHYSICAL REVIEW LETTERS

1:0cos
0:925

2cos < 0:075
cos  0:075:(1)

The resulting neutrino effective areas, the equivalent area
at Earth’s surface in which neutrinos are detected with
100% efﬁciency, averaged over the two-year period fromMay 2010 to May 2012 taking into account the different
detector conﬁgurations, is shown in Fig. 3. The analysis
starts to be sensitive in the energy region around 1 PeVwith its sensitivity rapidly increasing with energy. The
effective area is larger for e than  or  below
10 PeV showing the sensitivity of the present analysis tocascade events in this energy region.
The expected numbers of background events in the ﬁnal
sample for the 615.9 day live time from atmospheric muonsand neutrinos from decays of pions and kaons are 0:038 þ0:0100:004ðstatÞþ0:021
0:038 ðsystÞ and 0:012  0:001ðstatÞ0:007 ðsystÞ,respectively. Compared to previous analyses, the utilized
atmospheric neutrino ﬂux models [12] accommodate an
improved parametrization of the primary cosmic ray spectrum and composition which accounts now for the ‘‘knee’’in the cosmic ray spectrum. Adding prompt atmospheric
neutrinos from decays of charmed mesons assuming
the model in [13] with the improved cosmic ray spectrum
modeling, the total number of background events
increases to 0:082  0:004ðstatÞþ0:041
0:057 ðsystÞ. Theoreticalneutrino effective area [m2]

PRL 111, 021103 (2013)

10000
1000
100
10

νe
νμ
ντ

1
0.1
0.01

5

6

7
8
log Eν /GeV

9

10

10

FIG. 3 (color online). The average neutrino effective area for a4 isotropic ﬂux, 615.9 days live time, and the IC79 and IC86
string conﬁgurations. Exposure of the sample used in thisanalysis is obtained by multiplying the effective area with thelive time and 4 solid angle. The sharp peak for  e is the
Glashow resonance [24].

uncertainties in our baseline charmed-meson model [13]which uses perturbative-QCD calculations are included in
the background estimation. Potential nonperturbative contributions, such as intrinsic charm in nuclei [14] or from thegluon density at small x, could lead to signiﬁcantly larger
cross sections and, hence, higher prompt neutrino ﬂuxes.
Preliminary IceCube limits on the prompt ﬂux at 90% C.L.
are a factor of 3.8 higher than the baseline model [15].
The main systematic uncertainties on the backgrounds
are from the measurement of NPE and from uncertainties
in the cosmic ray ﬂux. They are estimated by varying theassociated parameters in the simulation. The two dominantsources of experimental uncertainties are the absolute
DOM sensitivity and the optical properties of the ice which
contribute with (þ 43%, 26%) and (þ 0%, 42%),
respectively. Uncertainties in the cosmic ray ﬂux models
are dominated by the primary composition (þ 0%, 37%)
and the ﬂux normalization (þ 19%, 26%). The theoretical uncertainty in the neutrino production from charm
decay [13] relative to the total background is (þ 13%,
16%). The systematic uncertainties are assumed to beevenly distributed in the estimated allowed range and aresummed in quadrature.
The atmospheric muon and neutrino background events
are simulated independently. However, at higher energies,
events induced by downward-going atmospheric neutrinos
should also contain a signiﬁcant amount of atmosphericmuons produced in the same air shower as the neutrino[16]. Since these events are reconstructed as downwardgoing, they are more likely to be rejected with the higher
NPE threshold in this region. Thus, the number of simulated atmospheric neutrino background events is likely
overestimated here.
After unblinding 615.9 days of data, we observe two
events that pass all the selection criteria. The hypothesisthat the two events are fully explained by atmospheric021103-4

19

PRL 111, 021103 (2013)

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PHYSICAL REVIEW LETTERS
103

data

102

E2φ = 3.6x10 GeV sr -1 cm-2 s-1
cosmogenic ν Yoshida

atmospheric μ

cosmogenic ν Ahlers

atmospheric ν prompt

sum of atmospheric background-8

Number of events

10

10

10-2

10-4
10-54.5

5

5.5

6

6.5

7

7.5

log NPE
10

FIG. 5 (color online). NPE distributions for 615.9 days of live
time at ﬁnal selection level. The black points are the experimental data. The error bars on the data show the Feldman-Cousins
68% conﬁdence interval [25]. The solid blue line marks the sumof the atmospheric muon (dashed blue), conventional atmospheric neutrino (dotted light green) and the baseline prompt
atmospheric neutrino (dotted-dashed green) background. The
error bars on the line and the shaded blue region are thestatistical and systematic uncertainties, respectively. The redline represents the cosmogenic neutrino model [11]. The shaded
region is the allowed level of the cosmogenic  ﬂux by Ahlers
et al. [26]. The orange line represents an E2 power-law ﬂux up
to an energy of 109 GeV with an all-ﬂavor normalization ofE2 e þ þ ¼ 3:6  108 GeV sr1 s1 cm2 , which is the integral upper limit obtained in a previous search in a similarenergy range [9]. The signal ﬂuxes are summed over all neutrino
ﬂavors, assuming a ﬂavor ratio of e : : ¼ 1:1:1.

photoelectrons in a given time interval and DOM for acascade hypothesis which depends on the interaction vertex, deposited energy and direction. Here, the time of
the ﬁrst hit mainly determines the vertex position and therecorded NPE plays a dominant role in estimating thedeposited energy. The hit information used in the reconstruction is extracted from an unfolding procedure of the
waveforms. The open circles in Fig. 1 indicate the strings
closest to the reconstructed vertex positions. The reconstructed deposited energies of the two cascades are 1.04
and 1.14 PeV, respectively, with combined statistical andsystematic uncertainties of 15% each. The errors on thedeposited energies are obtained by simulating cascade
events in the vicinity of the reconstructed energies andvertices. The study is speciﬁcally performed on each eventand the larger of the two event uncertainties is cited forboth events. Thus, the error associated with the two events
differs from that of other cascade events observed in
IceCube [19]. Since there is no absolute energy standard
with adequate precision at these energies, the energy scale
is derived from simulations based on measured ice
properties and photomultiplier tube efﬁciencies which
are assured by measurements of atmospheric muons.
The main sources of systematic uncertainty on the021103-5

20

1
-1

10-3

FIG. 4 (color online). The two observed events from(a) August 2011 and (b) January 2012. Each sphere represents
a DOM. Colors represent the arrival times of the photons where
red indicates early and blue late times. The size of the spheres isa measure for the recorded number of photoelectrons.

background including the baseline prompt atmospheric
neutrino ﬂux [13] has a p value of 2:9  103 (2:8 ).
This value includes the uncertainties on the expected number of background events by marginalizing over a ﬂat error
distribution. While the prompt component has large theoretical uncertainties, obtaining two or more events with aprobability of 10% would require a prompt ﬂux that isabout 15 times higher than the central value of our
perturbative-QCD model. This contradicts our preliminary
upper limit on the prompt ﬂux [15]. Using an extreme
prompt ﬂux at the level of this upper limit, which covers
a potential unknown contribution from intrinsic charm[17], yields a signiﬁcance of 2:3 .
The two events are shown in Fig. 4. They are from theIC86 sample, but would have also passed the selection
criteria of the IC79 sample. Their spherical photon distributions are consistent with the pattern of Cherenkov
photons from particle cascades induced by neutrino interactions within the IceCube detector. There are no indications for photons from incoming or outgoing muon or tau
tracks. Hence, these events are most likely induced byeither CC interactions of e or NC interactions of e ,  ,or  . CC interactions of  induce tau leptons with mean
decay lengths of about 50 m at these energies [18]. The
primary neutrino interaction and the secondary tau decay
initiate separate cascades which, in a fraction of such
events, lead to an observable double-peak structure in therecorded waveforms. The two events do not show a signiﬁcant indication of such a signature. Figure 5 shows theﬁnal-selection NPE distributions for the experimental data,
signal models, and background simulations. The two
events are near the NPE threshold of the analysis and areconsistent with a previous upper limit by IceCube [9] on an
unbroken E2 ﬂux, while a ﬂux corresponding to this upper
limit predicts about 10 events above the NPE cut. The
cosmogenic neutrino model [11] predicts an event rate ofabout 2 events in the corresponding live time but at signiﬁcantly higher energies.
Maximum-likelihood methods are used to reconstruct
the two events. The likelihood is the product of the Poisson
probabilities to observe the recorded number ofatmospheric ν conventional

PRL 111, 021103 (2013)

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PHYSICAL REVIEW LETTERSTABLE I. Characteristics of the two observed events. The depths of the reconstructed vertex
positions ‘‘z’’ are with respect to the center of the IceCube detector at a depth of 1948 m.
Date (GMT)

August 8, 2011

January 3, 2012

7:0  104

9:6  104312
1:14  0:17
25  5

NPE
Number of recorded DOMs
Reconstructed deposited energy (PeV)
Reconstructed z vertex (m)354
1:04  0:16
122  5reconstructed deposited energies are the absolute DOM
sensitivity and the optical properties of the ice [20]. The
effect of the latter is estimated to be þ9% and 5% and is
obtained by varying the scattering and absorption coefﬁcients for the photon propagation by 10%. The reconstruction algorithm includes variations of the scattering andabsorption coefﬁcients with depth (ice layers) [21]. The
effect of a possible azimuthal anisotropy of the ice parameters and a tilt of the ice layers on the reconstructed energies
is estimated to be 5%. The reconstructed energy depends
linearly on the DOM efﬁciency, which has a 10% systematic uncertainty. The suppression of bremsstrahlung andpair production due to the Landau-Pomeranchuk-Migdal
effect [22] is negligible in this energy range. The propertiesof the two observed events are summarized in Table I.
The reconstructed deposited energy is the energy of theincoming neutrino if the observed cascade is the result of a
CC interaction of the e neutrino, as in this case the total
neutrino energy is deposited near the interaction vertex[23]. On the other hand, NC interactions of neutrinos ofany ﬂavor or interactions of  e via the Glashow resonanceat 6.3 PeV [24] with outgoing leptons induce cascades
which carry only a fraction of the neutrino energy. The
observed cascades are unlikely to originate from the
Glashow resonance as only about 10% of these interactions
will deposit 1.2 PeV or less in the detector in cascadelike
signatures.
The two PeV neutrino events observed in two years ofdata taken with the IceCube neutrino telescope may be aﬁrst hint of an astrophysical high-energy neutrino ﬂux.
Given the yet rather moderate signiﬁcance of 2:8 withrespect to the expected atmospheric background and thelarge uncertainties on its prompt component, a ﬁrm astrophysical interpretation requires more data in combination
with analyses in other detection channels and energy
ranges.
We 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 Alumni 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;

Natural Sciences and Engineering Research Council of
Canada, Compute Canada, and Compute West High
Performance Computing; Swedish Research Council,
Swedish Polar Research Secretariat, Swedish National
Infrastructure for Computing (SNIC), and Knut andAlice Wallenberg Foundation, Sweden; German Ministry
for Education and Research (BMBF), Deutsche
Forschungsgemeinschaft (DFG), Helmholtz Alliance for
Astroparticle Physics (HAP), Research Department of
Plasmas with Complex Interactions (Bochum), Germany;
Fund for Scientiﬁc Research (FNRS-FWO), FWO
Odysseus programme, Flanders Institute to encourage
scientiﬁc and technological research in industry (IWT),
Belgian Federal Science Policy Ofﬁce (Belspo);
University of Oxford, United Kingdom; Marsden Fund,
New Zealand; Australian Research Council; Japan
Society for Promotion of Science (JSPS); the Swiss
National Science Foundation (SNSF), Switzerland.

*Also at Physics Department, South Dakota School ofMines and Technology, Rapid City, South Dakota
57701, USA.
†
Also at Los Alamos National Laboratory, Los Alamos,
New Mexico 87545, USA.
‡
Corresponding author.
aya@hepburn.s.chiba-u.ac.jp§
Also at Sezione INFN, Dipartimento di Fisica, I-70126
Bari, Italy.
∥
Also at Department of Physics, Sungkyunkwan University,
Suwon 440-746, Korea.
¶
Also at NASA Goddard Space Flight Center, Greenbelt,
Maryland 20771, USA.
[1] A. Achterberg et al. (IceCube Collaboration), Astropart.
Phys. 26, 155 (2006).
[2] R. Abbasi et al. (IceCube Collaboration), Astropart. Phys.
35, 615 (2012).
[3] R. Abbasi et al. (IceCube collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A 618, 139 (2010).
[4] R. Abbasi et al. (IceCube collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A 601, 294 (2009).
[5] R. Abbasi et al. (IceCube Collaboration), Phys. Rev. D 82,
072003 (2010).
[6] J. Ahrens et al., Nucl. Instrum. Methods Phys. Res., Sect.
B 524, 169 (2004).
[7] P. Huber, Robust Statistics (Wiley, New York, 1981).

021103-6

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PRL 111, 021103 (2013)

PHYSICAL REVIEW LETTERS[8] M. Wellons et al., Proceedings of the 33rd International
Cosmic Ray Conference (ICRC2013) (2013) (to be
published).
[9] R. Abbasi et al. (IceCube Collaboration), Phys. Rev. D 83,
092003 (2011).
[10] G. Hill and K. Rawlins, Astropart. Phys. 19, 393(2003).
[11] S. Yoshida and M. Teshima, Prog. Theor. Phys. 89, 833(1993), the model with the source evolution ðzmax þ 1Þm
with m ¼ 4 extending to zmax ¼ 4:0.
[12] T. K. Gaisser, Astropart. Phys. 35, 801 (2012).
[13] R. Enberg, M. H. Reno, and I. Sarcevic, Phys. Rev. D 78,
043005 (2008).
[14] S. Brodsky, P. Hoyer, C. Peterson, and N. Sakai, Phys.
Lett. 93B, 451 (1980).
[15] A. Schukraft (IceCube Collaboration), arXiv:1302.0127.
[16] S. Schönert, T. K. Gaisser, E. Resconi, and O. Schulz,
Phys. Rev. D 79, 043009 (2009).
[17] M. Thunman, G. Ingelman, and P. Gondolo, Astropart.
Phys. 5, 309 (1996).

[18] D. Cowen (IceCube Collaboration), J. Phys. Conf. Ser. 60,
227 (2007).
[19] R. Abbasi et al. (IceCube Collaboration), Phys. Rev. D 84,
072001 (2011).
[20] M. Aartsen et al., Nucl. Instrum. Methods Phys. Res.,
Sect. B 711, 73 (2013).
[21] J. Lundberg, P. Miočinović, K. Woschnagg, T. Burgess, J.
Adams, S. Hundertmark, P. Desiati, and P. Niessen, Nucl.
Instrum. Methods Phys. Res., Sect. A 581, 619 (2007).
[22] L. Gerhardt and S. R. Klein, Phys. Rev. D 82, 074017(2010).
[23] The energy reconstruction assumes that all light emission
originates from an electromagnetic shower. A hadronic
cascade with the same light yield as the observed eventswould, on average, have about 10% higher energy.
[24] S. L. Glashow, Phys. Rev. 118, 316 (1960).
[25] G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873
(1998).
[26] M. Ahlers, L. A. Anchordoqui, M. Gonzalez-Garcia, F.
Halzen, and S. Sarkar, Astropart. Phys. 34, 106 (2010).

021103-7

22week ending
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PHYSICAL REVIEW D 85, 063002 (2012)

Constraints on the origin of the ultrahigh energy cosmic rays using cosmic diffuse
neutrino ﬂux limits: An analytical approach
Shigeru Yoshida* and Aya Ishihara†
Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan(Received 12 January 2012; published 15 March 2012)
Astrophysical neutrinos are expected to be produced in the interactions of ultrahigh energy cosmic rays
with surrounding photons. The ﬂuxes of the astrophysical neutrinos are highly dependent on thecharacteristics of the cosmic-ray sources, such as their cosmological distributions. We study possible
constraints on the properties of cosmic-ray sources in a model-independent way using experimentallyobtained diffuse neutrino ﬂux above 100 PeV. The semianalytic formula is derived to estimate thecosmogenic neutrino ﬂuxes as functions of source evolution parameter and source extension in redshift.
The obtained formula converts the upper limits on the neutrino ﬂuxes into the constraints on the cosmicray sources. It is found that the recently obtained upper limit on the cosmogenic neutrinos by IceCube
constrains the scenarios with strongly evolving ultrahigh energy cosmic-ray sources, and the future limits
from a 1 km3 scale detector are able to further constrain the ultrahigh energy cosmic-rays sources withevolutions comparable to the cosmic star formation rate.
DOI: 10.1103/PhysRevD.85.063002

PACS numbers: 98.70.Sa, 95.75.Pq, 95.85.Ry

I. INTRODUCTION
The origin of the ultrahigh energy cosmic rays
(UHECRs) has been a long-standing important questionin astrophysics. While the observations by Auger [1,2] and
HiRes [3] indicate that cosmic rays with energies above
1018:5 eV are of extragalactic origin, identiﬁcation ofastronomical objects responsible for the UHECR emission
has not been achieved. Neutrinos, secondarily produced by
UHECR nucleons, are expected to provide direct information on the UHECR origin, since a neutrino penetrates overcosmological distance without being deﬂected by the cosmic magnetic ﬁeld nor absorbed by the photon ﬁeld. The‘‘cosmogenic’’ neutrinos [4] are produced by the collisionsof UHECR nucleons with the cosmic microwave background (CMB) photon via photo-produced  meson decayas  !   ! e e  , known as the GreisenZatsepin-Kuzmin (GZK) mechanism [5]. The intensity ofcosmogenic neutrinos indicates redshift distributions of theparent UHECR sources [6,7] in the Universe. The source
distributions derived from the cosmogenic neutrino intensities can then be compared with distributions of knownclasses of the astronomical objects possibly responsible
for the UHECR emissions. Therefore reliable extractionsof the UHECR source distribution function (SDF) is one of
the key issues in cosmogenic diffusive neutrino searches.
Constraints on the sources of UHECRs derived from themeasurements or upper limits of the ultrahigh energy
neutrino ﬂux are highly complimentary to the constraints
from the diffuse photon ﬂux [8,9], because the former does
not rely on uncertain estimation of extragalactic background light (EBL).
*syoshida@hepburn.s.chiba-u.ac.jp†
aya@hepburn.s.chiba-u.ac.jp

1550-7998= 2012=85(6)=063002(9)In this work, we develop a method to bound the UHECR
source evolution and its redshift dependence in a comprehensive way without introducing speciﬁc astronomical
models. We derive an analytical formula to calculate intensities of the neutrinos produced by the GZK mechanism in
the range between 100 PeV and 10 EeV. Using the formula,
we extract the relation among the neutrino intensity and the
UHECR SDF parameters. The use of the analytical formula
allows us to calculate neutrino intensities in the full phasespace of the source evolution parameters without an intensive computational task. The analytical formula can also be
used as a practical tool to approximately calculate cosmogenic GZK neutrino intensity with given UHECR SDF,
for example, for the performance studies of the future
detectors such as KM3NET [10]. Finally we present
model-independent constraints on the UHECR sources using the obtained formula with the upper limit [11] and thefuture sensitivity [12] on the cosmogenic neutrino detection
by the IceCube neutrino observatory [13].
The standard cosmology with H0 ’73:5 kmsec1 Mpc1 ,M ¼ 0:3, and  ¼ 0:7 [14] is assumed throughout the
paper.
II. ANALYTICAL FORMULA FOR ESTIMATINGCOSMOGENIC  INTENSITY
The neutrino ﬂux per unit energy, dJ =dE , is generally
written as







Z zs 
Z zmax




dJ
dt

 dt





¼ n0 cc ðzs Þ
Þ
Þ
ðz
ðz
dz
dz




s
s





dz
dz

 
dE
0





Z 1 dNp!

0ggg g ðz ; zs ÞðE  ð1 þ z ÞE ÞdE :E dE dt(1)

The ﬁrst integral represents the total contribution of
UHECR sources in the redshift up to zmax , where zmax is063002-1

Ó 2012 American Physical Society

23

SHIGERU YOSHIDA AND AYA ISHIHARAPHYSICAL REVIEW D 85, 063002 (2012)

the maximum redshift of the UHECR source distribution
or, in other words, the time of the ﬁrst UHECR emission in
the Universe. c ðzs Þ represents the cosmic evolution of thespectral emission rate per comoving volume and n0 is thenumber density of UHECR sources at the present Universe.
The relation between time and redshift is given as
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
dt
dt
j ðzs Þj  j s j ¼ ½H0 ð1 þ zs Þ M ð1 þ zs Þ3 þ  1 :dzs
dz
The second integral calculates the total neutrino ﬂux
expected from a single UHECR source at redshift zs
generated via UHECR interactions at redshift z ð zs Þ.
dNp! =dEg dtg is the yield of generated neutrinos withenergy of Eg per unit time in the UHECR laboratory frame(the CMB rest frame). Sufﬁxes s and g represent thequantities at the positions of UHECR sources and neutrino
generation, respectively. The delta function indicates theneutrino energy loss due to the expansion of the Universe.
The neutrino yield, dNp! =dEg dtg , at redshift z by the
GZK mechanism is expressed by a convolution of the
UHECR intensity from a source at zs , the CMB photon
density, and the photo-pion interaction kinematics as
Z
Z
dNp!
dN
dECR CR ðzs ; z Þc ds
g g ¼
dE dtdECR
Z
d p d ! dn
;
(2)
 dE
dE dEg ds
where dNCR =dECR is the number of UHECRs per unit timeand energy at the redshift z originating from a source at zs ,and s is the Lorentz-invariant Mandelstam variable, thesquare of invariant mass of the cosmic-ray nucleon and thetarget CMB photon. p is the photo-pion production crosssection, d ! =dEg is the energy distribution of neutrinos
from the photo-produced pion, and dn =ds is the CMB
photon number density in the UHECR frame per unit s.
We introduce the following approximations to simplify
the calculations: (1) the contribution of UHECR colliding
with infrared and optical universal photon (IR/O) backgrounds is negligible and only the contribution of photopion production cross section from  resonance is considered
in collisions of UHECRs and CMB photons, and (2) the
kinematics of the photo-pion production is represented bya single pion production. The ﬁrst approximation allows
the photon number density dn =ds to be analyticallyobtained with the modiﬁcation to the black-body distribution [6]. The contribution of neutrinos induced by
UHECR interactions with IR/O becomes sizable only inthe energy region below 100 PeV [15] while the effect issmall in the higher energy region. Similarly the neutrinos
from photo-produced pions outside the  resonance aremostly visible only in the lower energy range below
100 PeV [16], and the single pion production is the mostdominant channel in the  resonance. The -resonanceapproximation simpliﬁes the integral on s in Eq. (2) to a
multiplication of the integrand at s ¼ sR ð’ 1:5 GeV2 Þ,

where sR is the Lorentz-invariant Mandelstam variable
at the  resonance, and sR ð’ 0:6 GeV2 Þ, the width of the resonance. The second approximation then gives [17]
1
3
d !
’
;
g
E
1

r
dE


where r ¼ m2 =m2 ’ 0:57 is the muon-to-pion masssquared ratio. The factor three arises from the fact thatthree neutrinos are produced from the  meson and 
lepton decay chain. The allowed range of Eg due to thekinematics is given by
0

Eg
E

1  r ;(4)

where neutrino mass is neglected. With a good approximation that a single pion is isotropically emitted in thecenter-of-momentum frame, one obtainsd p
1 d p1p¼’;
ECR dx
ECR xþ  x
dE

(5)

where x  E =ECR is the relative energy of emitted pion
normalized by the parent proton energy ECR . x are themaximal and minimal bound of x due to the kinematics
and given by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2  m2ðs þ m2  m2p Þ2  4sm2
s
þ
m

p
x ¼
; (6)

2s
2s
where mp is the proton mass.
Then we obtain the neutrino yield, Eq. (2), expressed as
an analytical function with only a single energy integral,
dNp! kB Tð1þz Þ’ðsR m2p Þ Rp
82 ℏ3 c2
dEg dtdsR sR3
 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ
1rðsR þm2 m2p Þ2 4sR m2
Z
1 dNCR dECR 3
ECR dECR þxln R flnð1eðE Þ=ð1þz ÞECR Þg:R(7)

Here kB is the Boltzmann constant, T is present temperature of the CMB. E  ðsR  m2p Þ=4kB T corresponds tothe energy of UHECR protons colliding via  resonance atthe present Universe. Sufﬁx R denotes the values at the 
resonance in the photo-pion reaction. For example, Rp ¼
2:1  1028 cm2 represents the photo-pion production
cross section of channel p ! nþ at the  resonanceand x
R is given by Eq. (6) with s ¼ sR .
The parameter R reﬂects the kinematics bounds,
Eqs. (4) and (6), and is deﬁned by

063002-2

24(3)

CONSTRAINTS ON THE ORIGIN OF THE ULTRAHIGH. . .

R ¼

8 
< xR
:

Eg
Eg

ð1r ÞECR

ð1  r Þx
R ECR ;

otherwise:(8)

dNCR =dECR is calculated by the energy loss formula withthe continuous energy loss approximation [18] represented
by


dECR
ð1 þ zÞ3¼
E ;cdt
GZK ðECR ð1 þ zÞÞ CR(9)where GZK is the energy attenuation length governed by
the GZK mechanism, mainly due to the photo-pion production of UHECRs and the CMB. The factor ð1 þ zÞ3
accounts for the increase of CMB photon number densitywith redshift z.
Here we introduce the ﬁnal approximation that theenergy attenuation length of UHECR by the GZK mechanism, GZK , is constant with energies above EGZK 
1020 eV. While GZK rapidly decreases with cosmic-ray
energy increase, it becomes a slight increase or constant
above 3  1020 eV for z 0. Neutrinos from z * 1
are the dominant contribution to the cosmogenic neutrino
intensity at Earth and the turnover energy is shifted tolower energies & EGZK due to the redshift effects for the
Universe of z * 1 [19]. Therefore this approximation
reasonably describes the UHECR energy loss proﬁle tocalculate the neutrino yield. Assuming that the primary
UHECR spectrum from a source at zs follows the powerlaw described by dNCR ðzs ;zs Þ=dECR ¼CR ðECR =EGZK Þ
up to Emax , the maximal injected energy from a source,then the dNCR ðzs ; z Þ=dECR is analytically obtained by


dNCR
E
ðzs ;z Þ ¼ CR CR
dECR
EGZK
 eð 1Þðc=GZK H0 Þð2=3M Þffðzs Þfðz Þg ; (10)pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
where fðzÞ  M ð1 þ zÞ3 þ  and CR is a normalization constant. With Eq. (10), the energy integral on ECR
inbecomes an additionRof integrals in the forms of
R Eq.ð(7)þ3Þ
lnð1  e1=y Þ and dyyð þ3Þ lnð1e1=y Þlny.
dyy
An asymptotic approximation with numerical constants isfound to provide approximate solutions of these integrals.
The ﬁnal formula of the neutrino yield is then obtained as


dNp!
kB T ðsR  m2p Þ E ð þ2Þ R
¼

CR
p
dEg dtg
EGZK
82 ℏ3 c2 E2GZKsR sR3
 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð1 þ z Þ þ3ﬃ
2
2 2
2 1  rðsR þ m  mp Þ  4sR m eð 1Þðc=GZK H0 Þð2=3M Þffðzs Þfðz Þg þx
 0 x0ð þ1Þ e2 ln R þ 1 x1ð þ3Þ e1=x1
xR


E
x
 e2 ln x1 g 
ð1

r
Þ
;
(11)

E ð1 þ z Þ R

PHYSICAL REVIEW D 85, 063002 (2012)

where x0 ¼ 0:275, and x1 ¼ 0:16 are the empirically determined numerical constants. 0 and 1 are either unity ornull, depending on neutrino energy. These are consequences of the kinematics bound for pions and neutrinos, Eq. (8),and given by
1 Egv ð1 þ zv Þ x1 E xþ
R ð1  r Þ;(12)¼
00 otherwise;and80 Egv ð1 þ zv Þ x1 E x
>R ð1  r Þ;<Egv ð1 þ zv Þ x1 E xþ
1 ¼ > 1 x1 E xR ð1  r Þ
R ð1  r Þ;:
0 otherwise:(13)

One can also ﬁnd that x1 E x
R ð1  r Þ in these equations
represents the effective energy of neutrinos from decay ofthe pions with kinematically allowed maximum (xþR ) andminimum (x)energiesfrom
resonanceinthepcolliRsion. The Eg ð1 þ z Þ ¼ E ð1 þ z Þ2 factor reﬂects the redshift dependence of the CMB temperature and the redshiftenergy loss of neutrinos at z .
Equation (1) with the Eq. (11) ﬁnally give the cosmogenic neutrino ﬂux with double integrals of redshift zs andz . The z integral is analytically solvable neglectingOððGZK H0 =cÞ2 Þ or higher order terms because the energy
attenuation length is much shorter than the cosmologicaltime dimension. Then the ﬁnal form of the cosmogenic
neutrino intensity is obtained asdJ
c kB T ðsR m2p Þ E ð þ2Þ R¼ ð 1ÞFCR
p
dE
EGZK
H0 82 ℏ3 c3 E3GZKsR sR3
 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ:ðsR þm2 m2p Þ2 4sR m2 1 r

(14)Here FCR represents the UHECR intensity above EGZK anddescribed byZ EmaxZ zmaxdt

 dNCRFCR ¼
dECR n0 cc ðzs Þðz ;0Þðzs Þdz s dECR s
dz
EGZK
0
’ n0 CR EGZK GZK =ð  1Þ2(15)

assuming that Emax
EGZK . FCR gives the normalizationof the neutrino ﬂux in the present formulation in Eq. (14). It
can be estimated by the observational data for actual
calculation.
 in Eq. (14) is the term which accounts for the redshiftdependence and is given by þZ zmaxð1 þ zs Þðmþ 1Þ
xð þ1Þ 2
¼
dzs pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
e ln R0 x0
3xR0M ð1 þ zs Þ þ 


E

x
ð1

r
Þ
;
þ 1 x1ð þ3Þ e1=x1 e2 ln x1E ð1 þ zs Þ2 R
(16)
where 0 and 1 are obtained by Eqs. (12) and (13),respectively, replacing z by zs . The cosmic evolution

063002-3

25

SHIGERU YOSHIDA AND AYA ISHIHARAPHYSICAL REVIEW D 85, 063002 (2012)

function c ðzs Þ is now parametrized as ð1 þ zs Þm suchthat the parameter m represents the ‘‘scale’’ of thecosmic evolution often used in the literature [20].
The integral on zs in Eq. (16) is analytically solvablepﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
when we use the fact that M ð1 þ zs Þ3 þ in most of the integral range. Finally we obtain theﬁnal form of the redshift-dependent part of the analyticalformula  as


 

 þ


1 ðð þmÞ=ð3ÞÞxE2ðM ð1þzup Þ3 þ Þm =3 x0ð þ1Þ ln R þx1ð þ3Þ eð1=x1 Þ ln x1
M
x
ð1r
Þ
þ

xR
m
m
E ð1þzup Þ2 R
 

 þ

x
E
2

x
ð1r
Þ
þ
ðM þ Þm =3 x0ð þ1Þ ln R ðM ð1þzdown Þ3 þ Þm =3 x1ð þ3Þ eð1=x1 Þ ln x1mxRE ð1þzdown Þ2 R

 ¼ e2(17)
where m  ð þ mÞ  3=2. zup and zdown are the maximum and minimum bounds of the redshifts, respectively. These
redshift bounds are associated with zmax in Eq. (1) but also depend on neutrino energies E due to kinematics of  decay
and the redshift energy loss. zup is given by
8>1
x1 E xþEv;>
R ð1  r Þ>
< x1 E þ
1=2 x1 E xþ
R ð1r Þ
Ev x1 E xþ
R ð1  r Þ;
1 þ zup ¼(18)
Ev xR ð1  r Þ
ð1þzmax Þ2>
þ>
x1 E xR ð1r Þ>: 1 þ zmax
Ev:2
ð1þzmax Þzdown is also given by Eq. (18) replacing xþ
R by xR .
See Appendix B for the case of the astronomical objectsof which cosmological evolution become constant above acertain redshift (see Ref. [21], for example).

III. VALIDITY OF THE ANALYTICAL FORMULA
The analytical formula for estimating cosmogenic
neutrino ﬂuxes [see Eqs. (14), (17), and (18)] is derived under
several assumptions. Here we demonstrate the applicabilityof the formula in estimating neutrino ﬂux in 100 PeV &E & 10 EeV which is the main energy range of several
cosmogenic neutrino searches [11,22]. In Table I, thecosmogenic neutrino integral ﬂux above 1 EeV obtainedby the analytical formula with
¼ 2:5 is presented.
We use the UHECR intensity FCR ð EGZK Þ ¼ 2:96
1021 cm2 sec1 sr1 in the present study, which is obtained
from the measurement of the HiRes experiment [3]. The
ﬂuxes obtained by the full numerical calculations with thesame or comparable source evolution parameters are also
listed for comparison. The values in each parameter subset
show an agreement within a factor of 2 for a comparable
evolution scenario in the wide range of parameter numbers.
Figure 1 presents the neutrino ﬂuxes obtained with thepresent analytical estimation and the full-blown numericalcalculations. The ﬂuxes calculated with the different techniques show the best agreement at 1 EeV, the centralenergy in the cosmogenic neutrino search with IceCube[11]. The present formula provides a reasonable estimate of
the neutrino ﬂux from 100 PeV to 10 EeV with uncertainty offactor of 2. Some deviations in the analytical formula fromthe full-blown numerical calculations arise mainly from theuncertainty in the intensity of the extragalactic UHECR
component allowed by the observed UHECR spectrum,and the accuracy of the approximations used in derivationof the analytical formula. We discuss these issues in Sec. V.

TABLE I. Cosmogenic neutrino ﬂuxes predicted by the modeldependent full numerical calculations and those given by thepresent analytical formula with the corresponding parameters on
source evolution. The numbers by the full calculations wereconverted to be the sum over all three neutrino ﬂavors from theoriginal when appropriate.
 ﬂux model
Yoshida and Teshima [6]m ¼ 2:0, zmax ¼ 2:0
Ahlers et al. [9]m ¼ 2:0, zmax ¼ 2:0(’’the minimal case’’)The analytical formulam ¼ 2:0, zmax ¼ 2:0
Kotera et al.[15]SFR1The analytical formulam ¼ 3:4ðz 1:0Þ
const. ð1 z 4ÞAhlers et al. [9]m ¼ 4:6, zmax ¼ 2:0(’’the best ﬁt’’)
The analytical formulam ¼ 4:6, zmax ¼ 2:0
Kalashev et al. [23]m ¼ 5:0, zmax ¼ 3:0
The analytical formulam ¼ 5:0, zmax ¼ 3:0
Kotera et al. [15]Faranoff-Riley type II
The analytical formulam ¼ 5:02ðz 1:5Þconst ð1:5 z 2:5Þ063002-4

26

Integral ﬂux
F ðE  1 EeVÞ [cm2 sec1 sr1 ]5:39  1018
1:85  1018
4:91  1018
1:07  1017
1:07  1017
3:39  1017
4:09  1017
7:38  1017
8:42  1017
6:74  1017
5:21  1017

CONSTRAINTS ON THE ORIGIN OF THE ULTRAHIGH. . .

PHYSICAL REVIEW D 85, 063002 (2012)

4.5
4

Zmax

3.5
10-17
3
2.5
2
10-18

1.5

neutrino intensity [cm-2 sr-1 sec-1]

10-16

5

1
0

1

2

3

4

5

m

FIG. 2 (color online). Integral neutrino ﬂuxes with energy
above 1 EeV, J ½cm2 sec1 sr1 , on the plane of the source
evolution parameters, m and zmax .

FIG. 1. Integral neutrino ﬂuxes, J ½cm2 sec1 sr1 , as afunction of neutrino energy. Bold lines represent the present
analytical estimates and thin lines represent corresponding predictions by the full numerical calculations [9] or the MonteCarlo simulations [6,15].

IV. RESULTS
A. The relation between the  ﬂux and the cosmologicalevolution of the sources
Shown in Fig. 2 is the distribution of the cosmogenic
neutrino integral ﬂuxes with energies above 1 EeV in theparameter space of the evolution of UHECR sources
ðm; zmax Þ calculated using the derived analytical formula.
The ﬂuxes vary by more than an order of magnitude withthe evolution parameters. The distribution demonstrates
that the neutrino intensity can indeed be an observable to
imply the characteristics of the UHECR sources. The plotshows that cosmogenic neutrino ﬂux around 1 EeV ismostly determined by source emissivity history up to
redshift of zs 3. This is because the contributions ofsources at zs * 3 represent only a small fraction of thetotal ﬂux due to the redshift dilution [15].
B. Constraints on UHECR origin with the IceCube
diffuse neutrino ﬂux limit
Here we estimate the expected event rates with the
IceCube neutrino observatory by using the derived analytical formula. The analytical function is valid in the IceCube
cosmogenic neutrino detection energy range distributed

around 1 EeV [11]. Convolution of Eq. (14) with the
IceCube neutrino effective area [11,12] gives the event
rate for the entire phase space of the evolution parameterm and the maximal redshift zmax . Full mixing in the standard
neutrino oscillation scenario is assumed and the intensity ofneutrinos of each of three neutrino ﬂavors corresponds to
one third of the estimated neutrino intensity by the analytical
function. The Feldman-Cousins upper bound [24] then deﬁnes the excluded region on the m  zmax plane at a given
conﬁdence level. Figure 3 displays the resultant constraints.
The shaded region represents the factor of 2 uncertainty inthe analytical estimation discussed in the previous section.
The upper limit with the IceCube 2008–2009 data [11] hasalready started to constrain hypotheses of UHECR sources
with strong evolution of m * 4:5. While this bound may be
still weaker than that by the Fermi diffuse -ray ﬂux measurement [9], nevertheless the limit by neutrinos is importantbecause the neutrino estimate does not involve the uncertainties of the assumptions of Emax nor the EBL intensity.
The full IceCube ﬁve-year observation would certainlyprobe the most interesting region of the source evolution
phase space where the strong candidates for the UHECR
sources of the powerful astronomical objects such as radiogalaxies and gamma-ray bursts are included.
V. DISCUSSION
The derived analytical formula to calculate intensities of
the neutrinos produced by the GZK mechanism in therange between 100 PeV and 10 EeV is used to constrain
the cosmological evolution of the UHECR sources.
The largest uncertainty in the present analytical formulaat the lower energy range (E
1 EeV) is due to theomission of the IR contribution to the cosmogenic neutrino
production. Photo-produced pions from the UHECR

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PHYSICAL REVIEW D 85, 063002 (2012)
5

5

4

4

4

3

4

Zmax

Zmax
5

1

3

2

2

2

.L.

1

3

.
C.L

2

90%

.
C.L

3

90% C

5

68%

Zmax

SHIGERU YOSHIDA AND AYA ISHIHARA

2

3

m

4

m

5

1

2

3

4

5

m

FIG. 3 (color online). Constraints on the UHECR source evolution m and zmax with the IceCube 2008–2009 ﬂux limit [11] (left) andwith the full IceCube ﬁve-year sensitivity [12] (middle). The areas above the solid lines are excluded by null detection of  events. The
shaded belts represent uncertainties in the present analytical estimation. The right panel shows the full IceCube ﬁve-year constraint
when the emission rate per comoving volume becomes constant above zs of 1.0. Excluded region at 68% conﬁdence level(corresponding to ’ 1:1 events assuming the same background rate of the IceCube 2008–2009 measurement [11]) and 90% conﬁdence
level ( ’ 2:2 events) is displayed.

interactions with the IR background are the major origin ofneutrinos with energies below 10 PeV, however, the IR
contribution is relatively minor in the higher energies where
we mainly discuss the aspect of cosmogenic neutrino detection by IceCube. The amount of the IR contribution wasstudied, for example, in the calculations in Refs. [9,15]. The
study in the latter reference exhibits much higher contribution of the IR background than in the former reference,
where the effect is suppressed mainly due to the introductionof the minimal energy of extragalactic UHECR population.
These differences can be seen in Fig. 1; the low energy
component in Ref. [15] is substantially emphasized compared to the other calculations. These variations in theestimation of the IR contribution to the cosmogenic neutrino
intensities are considered to be an additional uncertainty to
the IR background yield itself, which is also not ﬁrmly
understood [19,25]. Here we would like to emphasize thatthe omission of the IR background leads to a conservative
constraint on the UHECR source evolution.
The second largest uncertainty is concerned with FCR ,the UHECR intensity above EGZK ’ 1020 eV. The works in
Refs. [9,26] allowed a sizable variation in the UHECR
intensity within 99% conﬁdence level of the statistical test
against the observed data. This indicates that an extreme
case of the UHECR intensity may lead to a large departurefrom the present estimate of the neutrino ﬂuxes. For instance, the difference of their estimate for the scenario of
ðm; zmax Þ ¼ ð2; 2Þ found in Table I arises from their assumption of very steep UHECR spectrum leading to a minimal
FCR estimation. This uncertainty is, however, expected to be
reduced in the future when the statistical uncertainties in theobservations of UHECRs and/or the systematic uncertainty
in the energy estimation are improved.
We would like to also emphasize that the neutrino intensity
below 10 EeV is not largely affected by the detailed behaviorof UHECR proton propagation in extragalactic space. This isbecause these neutrinos are mostly generated at cosmological distances which are substantially longer than the UHECR
proton energy attenuation length in the CMB ﬁeld. It is alsosuggested by no explicit dependence of GZK in the ﬁnal
formula Eq. (14). This is related to the fact that the cosmogenic ﬂux below 10 EeV is relatively insensitive to Emax and, the maximal injection energy of UHECR protons fromtheir sources and the spectral index of UHECR spectrum,
respectively, while the ﬂux above 10 EeV is sensitive to thoseparameters [6,19,23]. A scan of the parameter spaces of thecosmogenic neutrino sources for some known classes ofastronomical objects with a numerical Monte-Carlo method
was made in Refs. [15,19]. It was also shown that theintensity around 1 EeV is stable against Emax variation andthe transition models between the Galactic and extragalactic
cosmic-ray components. These observations are consistent
with the fact that the neutrino intensities around 1 EeV by the
relatively old works [6,16] assuming harder UHECR spectrum of ¼ 2:0 and higher Emax , and those by the recent
works [9,15] with
2:5 show an agreement also within afactor of 2. The difference between the present analyticalformula and the full-blown simulation above 10 EeV in
Fig. 1 is attributed to responses to Emax . The present analytical estimates of neutrino ﬂuxes for 100 PeV & E &10 EeV, the main energy range by the IceCube cosmogenic
neutrino search, is robust against these parameters. We
should note however that we use FCR for the normalization
EGZK . If Emax is comparable orconstant assuming Emaxlower than EGZK , the neutrino yield strongly depends on Emax
and the present simple treatment is not capable of providing
reasonable estimates of the cosmogenic neutrino ﬂuxes.
The present analysis indicates that a ﬁve-year observation by the IceCube observatory will scan the source
evolution parameter space of the most interest where

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CONSTRAINTS ON THE ORIGIN OF THE ULTRAHIGH. . .

PHYSICAL REVIEW D 85, 063002 (2012)

many of the proposed UHECR astronomical sources are
distributed. A null neutrino observation then would imply
that either UHECR sources are only locally distributed(zmax & 1), very weakly evolved (m & 3), or the masscomposition of UHECRs is not dominated by proton primaries, but by heavier nuclei such as irons after all. The
ﬁrst two possibilities may lead to a speculation about thehighest energy particle emission from an entirely different
and probably dimmer class of objects than currently suggested. The last possibility has also been discussed with themeasurement of the depth of maximum of air-showers by
the Auger Collaboration [27]. A neutrino search in ultrahigh energies provides a complementary constraint on the
proton fraction of UHECRs in this case [28].

measurement on extragalactic diffuse -ray background[31]. In this work, the neutrino ﬂux was approximately
estimated by the energetics argument, calculating energy
channeling into secondary neutrinos from a UHECR proton during its propagation in the CMB ﬁeld. The neutrino
ﬂux is then calculated by


 dt

Z zmaxdJE  ¼ n0 c
dzs c ðzs Þ
Þ
ðz


s


dz

dE
0
Z
dNCR
d
R ðECR Þ  : (A1) dECR ECR
dECR
dE

VI. SUMMARY
We have derived the analytical formula to estimate thecosmogenic neutrino ﬂuxes for a wide range of cosmological evolution parameters of UHECR emission sources. The
analytical formula provides a practical tool for estimating
the neutrino intensity at around the EeVenergy region with alimited accuracy within a factor of 2. The obtained analytical estimates have indicated that the present IceCube
neutrino limit in 100 PeV–10 EeV energies disfavors the
scenarios with the strongly evolved UHECR sources. The
future IceCube observation will be able to scan most of
the interesting parameter space of UHECR source evolution.
Furthermore, while the deep and highly energetic part of
Universe is inaccessible with photons or cosmic rays due tothe CMB ﬁeld, the current study implies that the neutrinos
can be used as a rare tool to probe the far Universe.
With the greater statistics of ultrahigh energy neutrino
detections by the future neutrino telescopes of 100 km2
areas, such as ARA [29] and ARIANNA [30], the analytical formula allows us to specify the astronomical classes ofultrahigh energy cosmic-ray sources. The pioneer prediction of the cosmogenic neutrinos in the 1960s [4] will
ﬁnally lead to revealing the characteristics of an UHECR
emission mechanism in the near future.
ACKNOWLEDGMENTS
We wish to acknowledge Kumiko Kotera for useful
discussions in preparations for this work. The authors
are also grateful to Markus Ahlers and Spencer Klein
for valuable comments on the manuscript. A. Ishihara
acknowledges support by the Research Fellowships of theJapan Society for the Promotion of Science for Young
Scientist. This work was supported in part by the Grantsin-Aid in Scientiﬁc Research from the JSPS in Japan.
APPENDIX A: THE FLUX CALCULATIONBASED ON ENERGETICS
Recently the possible upper limit on the cosmogenic
neutrino ﬂux has been discussed solely using the Fermi

Here dNCR =dECR is the injected UHECR proton spectrum( Ep ) at the source redshift zs , R is a fraction of
UHECR proton injection energy carried by the secondary
neutrinos, and d  =dE is a distribution of neutrino energy. R was calculated in the earlier work [16] represented
by a numerically ﬁtted function as
R ¼

1þ



0:45

2 :

(A2)

21011 GeV
ð1þzs ÞECRWhile the original work [31] represented d  =dE asðE  ECR =ð20ð1 þ zs ÞÞÞ approximating each secondary neutrino receiving 1=20 of the UHECR proton energy,
we found that the single pion kinematics approximation
would give a better agreement in the neutrino spectral
shape with those obtained by the full-blown simulation.
It is then written as
 þ
d 
x
þ

1
’ ð1 þ zs Þ½ECR ðxR  xR Þð1  r Þ ln R ; (A3)dER
where R is given by Eq. (8), replacing Eg with E ð1 þ zs Þ.
This approach has an advantage in that it does not relyon the -resonance approximation. Although we are notable to ﬁnd out a complete analytical solution of theintegrals in Eq. (A1), the numerical calculations indeed
conﬁrmed that Eq. (A1) reasonably reproduces the full
simulation/numerical calculation results. It gives a better
agreement than our formula at around 100 PeV, owing toinclusion of direct pion production yielding a pair ofþ  by Eq. (A2) [16]. However, this energetics-based
formulation signiﬁcantly overestimates neutrino intensities
with energy above 1 EeV. We suspect this is due to neglecting of the energy loss of UHECR protons. Energy of an
UHECR proton is in many cases largely lower than its
injected energy when it yields neutrinos, because of energy
loss by the photo-pion production during the UHECR
propagation. Without accounting for this effect, higher
energy neutrino production is overweighted in the formulation. The overproduced high-energy neutrinos are thenredshifted and accumulated even in the PeV regime when
UHECR sources are strongly evolved. As a consequence,the estimated intensity departs from the calculation withthe full-blown simulation in case of the strong evolution
scenario. Since the GZK neutrino search by the IceCube

063002-7

29

SHIGERU YOSHIDA AND AYA ISHIHARAPHYSICAL REVIEW D 85, 063002 (2012)detector is sensitive to the EeV range and to emission
from strongly evolved sources, we concluded that theenergetics-based formulation is not appropriate for our
purpose.

of sources is written as c ðzs Þ ð1 þ zs Þm for 0 zs z~
and c ðzs Þ ð1 þ z~Þm for z~ zs zmax . The redshiftdependence term  (Eq. (16)) is then obtained with minor
modiﬁcations on Eq. (17) and given as

APPENDIX B: THE ANALYTICAL FORMULA FOR
THE PARTIALLY CONSTANT SOURCEEVOLUTION~ ¼ z~ þ ;

Some classes of astronomical objects, like galaxy starformation, seem to exhibit evolution nearly constant above
a certain redshift. For these cases, cosmological evolution

where z~ is given by Eq. (17) by replacing zmax with z~,
accounting for the evolution up to zs z~.
The additional term ~ is obtained in functions similar toEq. (17) as



 þ
1
xR
=3Þ
m
3
 =3 ð þ1Þ
x
~ ¼ e2 ð
ð1
þ
z
~
Þ
ð1
þ
z
~
Þ
þ

Þ
ln
ð
M
up

0
x
 M
R
 


 þ
E
2
x
ð þ3Þ ð1=x1 Þð þ1Þ

3

=3
þ x1
ln x1
 ðM ð1 þ z~down Þ þ  Þex ð1  r Þ þ
x0
ln R
xR

E ð1 þ z~up Þ2 R
 


E
2
 ðM ð1 þ z~down Þ3 þ  Þ =3 x1ð þ3Þ eð1=x1 Þ ln x1;x ð1  r Þ þE ð1 þ z~down Þ2 R
where  

(B1)

(B2)

 32 and the redshift bound z~up is given by
8
1 þ z~
>
>
>
1=2
<
x1 E þ1 þ z~up ¼
x
ð1

r
Þ

R
E
>
>
>
:
1 þ zmax

x1 E xþR ð1r Þ
ð1þ~zÞ2
x1 E xþð1rÞRð1þzmax Þ2

E

E ;
x1 E xþR ð1r Þ
;
ð1þ~
zÞ2

E

x1 E xþR ð1r Þ
ð1þzmax Þ2

(B3)

:


z~down is written as the same equation (B3) by replacing xþ
R with xR .

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072003 (2010).
[23] O. E. Kalashev, V. A. Kuzmin, D. V. Semikoz, and
G. Sigl, Phys. Rev. D 66, 063004 (2002).
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[27] J. Abraham et al. (Pierre Auger Collaboration) Phys. Rev.
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79, 083009 (2009).
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112 (2011).

063002-931

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)32092003-1

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 E2 spectrum in the energy range
2:0  106  6:3  109 GeV to a level of E2  3:6  108 GeV cm2 sec1 sr1 .
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  
104 GeV2 sec1 sr1 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 105 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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CONSTRAINTS ON THE EXTREMELY-HIGH ENERGY . . .

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 wasdeﬁned 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.

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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
(a)

105

2

10
10
1
10-1
10-2
-3

10

10-4
3.5

4

4.5 5 5.5 6log (NPE)
10

6.5

7

10
103
102
10
1

Number of Events

103

105

(c)

-1

10

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

103
10
1
10-1
10-2
10-3

10-4

10-4

4

4.5

5 5.5 6log10 NPE

6.5

7

(d)

102

10-3

cos (zenith angle)

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

104

102

4

Number of Events

Number of Events

104

103

(b)

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, zðt10 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

0

1000

2000

3000

4000

Δ 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) tLNE 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

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

103

102

102

10
1
0

10-1
10-2

-0.5

10-3
10

-1

4

5
6
log10 NPE

74000

Δ tLN-E[nsec]

10-2

-0.5

10-3
10-4

4000

4

5
6
log10 NPE

7

10-5

102
10
1
10-1

2000

10-2

10-3

10-3

10-4

10-4

-5

7

10-1

102

10-2

5
6
log10 NPE

1
0

-1

10-1

4

10

10-5

1

0

0.5

-4

10

2000

cos (zenith angle)

0.5

104

1

Δ tLN-E[nsec]cos (zenith angle)

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, tLNE , 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 tLNE 0 ns. The high rate in theexperimental data for tLNE  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 tLNE 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 tLNE vs NPE for the deep events.
Optimization is performed by differentiating the NPE
threshold numbers in the region cos 0:3 or tLNE
0:5 s for the shallow and deep quality bright sample,
respectively. The NPE threshold of the other region( cos  0:3 or tLNE  0:5 s) is conservatively determined such that the number of background events above thethreshold is less than 104 of the full live time for each binof cos with width 0.2 or 1 s for tLNE . 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

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
0:075

1:8  0:007
1:2  0:006

Quality
Final092003-5

36

Shallow
0:76  0:005
0:39  0:004þ0:054
0:043

Deep
0:43  0:004
0:18  0:002þ0:025
0:020

R. ABBASI et al.

PHYSICAL REVIEW D 83, 092003 (2011)

threshold value is 2:5  104 . 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 least2  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.
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 theﬁnal 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 E2 energy spectrum, this implies an integral ﬂux
limit of E2  3:6  108 GeV cm2 sec1 sr1 with thecentral 90% of the E2 signal found in the energy interval

092003-6

37

CONSTRAINTS ON THE EXTREMELY-HIGH ENERGY . . .

PHYSICAL REVIEW D 83, 092003 (2011)

-4

106

10-4

106

(a)

GZK 1

(b)

GZK 4
GZK 5

-6
10-6

WB bound

-8

10-8

1

the full IceCube(3 years)

IC-22

10-2

ANITA

10

102

1

7

PAO

8

9

7

8

(c)

10
104

FIG. 3 (color online). All ﬂavor neutrino ﬂux differential limit
and E2 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 E2 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

AMANDA

4

10-2

10

log Eν e /GeVRICEντ + 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 (assuminge : : : 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

38

104

IC-40 (333.5 days)

-9

-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

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 E2
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 Ee 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 ScientiﬁcResearch (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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092003-940

PHYSICAL REVIEW D 82, 103012 (2010)

Constraints on neutrino-nucleon interactions at energiesof 1 EeV with the IceCube Neutrino Observatory
Shigeru Yoshida*
Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan(Received 8 September 2010; published 22 November 2010)
A search for extremely high energy cosmic neutrinos has been carried out with the IceCube Neutrino
Observatory. The main signals in the search are neutrino-induced energetic charged leptons and their ratedepends on the neutrino-nucleon cross section. The upper limit on the neutrino ﬂux has implications forpossible new physics beyond the standard model such as the extra space-time dimension scenarios whichlead to a cross section much higher than the standard particle physics prediction. In this study we constrain
the neutrino-nucleon cross section at energies beyond 109 GeV with the IceCube observation. The
constraints are obtained as a function of the extraterrestrial neutrino ﬂux in the relevant energy range,
which accounts for the astrophysical uncertainty of neutrino production models.
DOI: 10.1103/PhysRevD.82.103012

PACS numbers: 98.70.Sa, 13.15.+g, 95.85.Ry

I. INTRODUCTION
High energy cosmic neutrino observations provide a rareopportunity to explore the neutrino-nucleon (N) interaction behavior beyond energies accessible by the present
accelerators. These neutrinos interact during their propagation in the Earth and produce energetic muons and taus.
These secondary leptons reach underground neutrino detectors and leave detectable signals. The detection rate is,therefore, sensitive to neutrino-nucleon interaction probapﬃﬃﬃ
bility. The center-of-mass energy of the collision, s, iswell above 10 TeV for cosmic neutrino energies on theorder of 1 EeV ( ¼ 109 GeV). This is a representative
energy range for the bulk of the GZK (Greisen-ZatsepinKuzmin) cosmogenic neutrinos, generated by the interactions between the highest energy cosmic ray nucleons andthe cosmic microwave background photons [1].
The N collision cross section can vary greatly if nonstandard particle physics beyond the standard
pﬃﬃﬃ model (SM)is considered in the high energy regime of s
TeV. The
extra-dimension scenarios, for example, have predicted
such effects [2,3]. In these scenarios, the virtual exchangeof the Kaluza-Klein graviton [2] or microscopic black hole
production [4] leads to a substantial increase of theneutrino-nucleon cross section by more than 2 orders ofmagnitude above the SM prediction. The effect would besizable enough to affect the expected annual event rate[Oð0:1  1Þ] of the GZK neutrinos in the km3 instrumentation volume of an underground neutrino telescope
such as the IceCube observatory. Thereby, the search for
extremely high energy (EHE) cosmic neutrinos leads toconstraints on nonstandard particle physics [5].
The IceCube neutrino observatory has already begun
EHE neutrino hunting with the partially deployed underground optical sensor array [6]. The 2007 partial IceCube*syoshida@hepburn.s.chiba-u.ac.jp
URL: http://www.ppl.phys.chiba-u.jp/~syoshida1550-7998= 2010=82(10)=103012(6)detector realized a 0:7 km2 effective area for muons with
109 GeV and recently placed a limit on the ﬂux of EHE
neutrinos approximately an order of magnitude higher thanthe expected GZK cosmogenic neutrino intensities with
242 days of observation [7]. Since new particle physics
may vary the cross section by more than an order ofmagnitude as we noted above, this result should already
imply a meaningful bound on the N cross section. In thispaper, we study the constraint on the N cross section( N ) by the null detection of EHE neutrinos with the2007 IceCube observation. A model-independent boundis derived by estimating the lepton intensity at the
IceCube depth with the SM cross section scaled by aconstant. The constraint is displayed in the form of the
excluded region on the plane of the cosmic neutrino ﬂux
and N . It is equivalent to an upper bound on N for agiven ﬂux of astrophysical EHE neutrinos. We also study
the model-dependent constraint on the microscopic blackhole creation by neutrino-nucleon collision predicted in theextra-dimension scenario [5]. We calculate the ﬂuxes of
leptons propagating in the Earth including the black holecross section and the ﬁnal states to estimate expected event
rate in an equivalent IceCube 2007 measurement as afunction of extraterrestrial neutrino intensity. The null
detection of signal candidates leads to a constraint on
this particular scenario.
There are several works on model-independent upperbounds of N using the observational limit of EHE neutrino ﬂux in the literature. References [3,4,8] derived thebound using the results of horizontal air shower search by
AGASA [9] and Fly’s Eye [10]. References [8,11] set thelimit based upon the ﬂux bound by the RICE experiment[12]. Our approach in the present study is different mainly
in two respects. The previous works assumed the GZK
cosmogenic neutrino bulk as the guaranteed beam anddeduced the cross section limit using the GZK neutrino
intensity. Here extraterrestrial neutrino intensity is considered a free parameter. This method is an application of the103012-1

Ó 2010 The American Physical Society

41

SHIGERU YOSHIDAPHYSICAL REVIEW D 82, 103012 (2010)

technique to derive the ﬂux limit based upon the quasidifferential event rate [7,12,13], which is independent ofspeciﬁc neutrino ﬂux models. It is valid when the cosmic
neutrino ﬂux and the cross section N do not rapidlychange over a decade of a given neutrino energy. As
EHE cosmic ray composition and their origin are still quite
uncertain, this approach provides more appropriate conservative limits on N . It also allows estimation of theminimum intensity of neutrino ﬂux required to constrain
the cross section. Another difference is that the previous
works introduced the simpliﬁcation that event rate solely
depends on rates of electromagnetic or hadronic cascades
directly initiated by neutrinos inside the effective volumeof the detector. This is in fact a good approximation for the
RICE experiment which is sensitive to radio emission fromshower events. However, underground neutrino telescopes
such as IceCube have larger effective areas for throughgoing muons and taus in EHE neutrino search [14–16].
This study of the model-independent limit includes calculation of not just intensities of neutrinos but also thesecondary muon and tau ﬂuxes reaching the detection
volume for a given N and includes their contributionsin the overall event rate.
The paper is outlined as follows: First we discuss themodel-independent constraint in Sec. II. The method to
calculate the neutrino and the secondary lepton propagation from the Earth’s surface to the IceCube detector depth
is described. The ﬂuxes for different strengths of N are
calculated and the resultant constraint is shown for both
N and the cosmic neutrino ﬂux at neutrino energies of 1
and 10 EeV, respectively. Section III describes the constraint on the microscopic black hole production by
neutrino-nucleon interaction as an example of the modeldependent bound on N . Fluxes of muons and taus from
evaporation of black holes produced in the neutrinonucleon collision in the Earth are calculated. Their contributions, as well as those from contained hadronic showers
induced directly by the evaporation, would give an observable event rate in the IceCube 2007 measurement, andthereby put constraints on the black hole scenario. We
summarize our conclusions in Sec. IV.
II. MODEL-INDEPENDENT CONSTRAINT ON THE
NEUTRINO-NUCLEON CROSS SECTION
The ﬂux limit obtained by the present IceCube observations allows us to place an upper bound on the neutrinonucleon cross section in a model-independent manner; newphysics cannot increase N too much, otherwise EHE
neutrinos would have produced observable events. As anunderground neutrino telescope is sensitive to not justshower events induced from neutrinos, but also tothrough-going muons and taus generated by the neutrinonucleon scattering, one must understand how much ﬂuxesof these leptons reaching an underground detection volume
is increased with N . In this section, we ﬁrst discuss our

method to calculate intensities of neutrinos, muons, andtaus at the underground depth of the IceCube observatory
for a wide range of N strength, followed by a descriptionof how they would contribute to the event rate. Finallythe constraint on both N and cosmic neutrino ﬂux is
described together with the relevant discussions.
A. The method
Given a neutrino ﬂux at the surface of the Earth, theneutrino and charged lepton ﬂuxes at the IceCube depth arecalculated by the coupled transportation equations [16]:
dJ
¼ NA
dX
þ NA
þ NA

dJl
¼ NA
dX

Z
Z

dE0

d

dE0l

d

ml Z
1 dndldEl
J ðE Þ
d
El dE l l
c l

N;NC

dE
lN;CC

dE

J ðE0 Þ

Jl ðE0l Þ;

(1)

ml
Jl
c dl ElZZddþ NA dE0 N;CC J ðE0 Þ þ NA dE0l lN Jl ðE0l Þ
dEl
dEl
d
ml Z
1
dn
dE0l 0 l Jl ðE0l Þ;(2)þEl dElc dl
lN Jl where Jl ¼ dNl =dEl and J ¼ dN =dE are differential
ﬂuxes of charged leptons (muons and taus) and neutrinos,
respectively. X is the column density, NA is the Avogadro’s
number, is the local density of the medium (rock/ice) in
the propagation path,is the relevant interaction crosssection, dndl =dE is the energy distribution of the decay
products which is derived from the decay rate per unit
energy, c is the speed of light, and ml and dl are themass and the decay life time of the lepton l, respectively.
CC(NC) denotes the charged (neutral) current interaction.
In this study we scale N to that of the SM prediction withthe factor Nscale , i.e., N  Nscale SMN . It is an extremely
intensive computational task to resolve the coupled questions above for every possible value of N . To avoid this
difﬁculty, we introduce two assumptions to decouple thecalculation of J from the charged lepton transportation
equation. The ﬁrst is that distortion of the neutrino spectrum by the neutral current reaction is small and the other isthat regeneration of neutrinos due to muon and tau decay
and their weak interactions is negligible. These are very
good approximations in the energy region above 108 GeV
where even tau is unlikely to decay before reaching the
IceCube instrumentation volume. Then the neutrino ﬂux issimply given by the beam dumping factor as

103012-2

42

N;CCþNC J þ

J ðE ; XIC Þ ¼ J ðE ; 0ÞeNscale N

SM;CC

XIC

;

(3)

CONSTRAINTS ON NEUTRINO-NUCLEON INTERACTIONS . . .

where XIC is column density of the propagation path fromthe Earth’s surface to the IceCube depth. The charged
lepton ﬂuxes, Jl¼; ðEl ; XIC Þ, are obtained asJ; ðE; ; XIC Þ ¼ NA


Z XIC

Z

0

dX

Z

dE0;

dE NscaledN; 0ðE ! E; ÞdE; ;d SM;CCN
dE0;

 J ðE ; 0ÞeNscale N

SM;CC

X

:

(4)

Here dN; =dE; ðE0; ! E; Þ represents distributionsof muons and taus with energy of E; at XIC created byN collisions at depth X with an energy E0; . This iscalculated in the transportation equation, Eq. (2), with areplacement of J ðE0 Þ by Eq. (3).
Calculation of the neutrino and the charged lepton ﬂuxes
with this method is feasible for a wide range of Nscale
without any intensive computation. A comparison of thecalculated ﬂuxes with those obtained without the introduced simpliﬁcation for a limited range of Nscale indicatesthat the relative difference we found in the resultant
J;; ðXIC Þ is within 40%. Since this analysis involves anorder of magnitude of increase in N , the introduced
approximations provide sufﬁcient accuracy for the present
study.
Figure 1 shows the calculated intensities of the secondary muons and taus for various Nscale factors. Here theprimary neutrino spectrum is assumed to follow the GZK
cosmogenic spectrum and ﬂux calculated in Ref. [17] assuming an all-proton cosmic ray composition with a moderately strong source evolution, ð1 þ zÞm with m ¼ 4
4

GZK ν

Flux [10 −18 cm−2 sec −1sr−1]

E > 10PeV

3

x10
2

1

x3
x1

0
−1

−0.5

0

0.5

1

cos (Zenith Angle)

FIG. 1 (color online). Integral ﬂuxes of the muon and taus
above 10 PeV ( ¼ 107 GeV) at IceCube depth ( 1450 m) for
GZK cosmogenic neutrinos [17]. The solid lines representmuons while the dashed lines represent taus. Numbers on eachof the curves are the multiplication factors (Nscale ) that enhance
the standard N cross section [19] in the relevant calculations.

PHYSICAL REVIEW D 82, 103012 (2010)

extending to z ¼ 4. One can see that the intensity is nearly
proportional to Nscale as expected since the interaction
probability to generate muons and taus linearly dependson N . It should be pointed out, however, that the dependence starts to deviate from the complete linearity when
the propagation distance is comparable to the mean freepath of neutrinos, as one can ﬁnd in the case of Nscale ¼ 10
in the ﬁgure. This is because the neutrino beam dumping
factor in Eq. (3) becomes signiﬁcant under thesecircumstances.
The ﬂux yield of leptons at the IceCube depth, Yl (l ¼
0 s, , ), originating from neutrinos with a given energy
at the Earth’s surface, Es , is given by Eq. (4) for muons andtaus and by Eq. (3) for neutrinos, with an insertion ofJ ðE ; 0Þ ¼ ðE  Es Þ. Here Es denotes a given incoming neutrino energy at the Earth’s surface. The resultant
event rate per neutrino energy decade is then obtained by[7,12,13],N ðEs Þ ¼

X
1 dJe þ þ s ZðE Þ d¼e ; ; 3 d logEl¼e ; ; ;;X

Z

dEl Al ðEl ÞYl ðEs ; El ; XIC ðÞ; Nscale Þ;(5)where Al is the effective area of the IceCube to detect the
lepton l. In the equation above, the l ¼ ,  terms represent the through-going track events while the contributionof events directly induced by neutrinos inside the detection
volume is represented by the terms l ¼ e ,  ,  . The
effective area for 0 s, A , is proportional to N i.e., Nscale
so the rate of contained shower events is linearly dependent
on the neutrino-nucleon scattering probability. Note thatthe differential limit of the neutrino ﬂux is given by Eq. (5)for Nscale ¼ 1 with N ¼ 
 90 which corresponds to the
90% conﬁdence level average upper limit. It calculates anupper bound of the number of events observed with bin
width of a decade of energy with the condition that energy
dependence of neutrino ﬂux multiplied by the effective
area behaves as 1=E [4,12]. Limiting N in the present
analysis corresponds to an extraction of the relation between Nscale and the (unknown) cosmic neutrino ﬂux
Je þ þ yielding N ¼ 
 90 . The obtained constraintson N is represented as a function of Je þ þ for agiven energy of Es . It consequently accounts for astrophysical uncertainties on the cosmic neutrino ﬂux.
In scenarios with extra dimensions and strong gravity,
Kaluza-Klein gravitons can change only the neutral current(NC) cross section because gravitons are electrically neutral. Any scenarios belonging to this category can beinvestigated by scaling only NC
N in the present analysis.
The event rate calculation by Eq. (5) is then performed forYl ðNscale ¼ 1Þ with the effective area for ’s, A , enhanced
þ Nscale SM;NC
Þ=ð SM;CCþ SM;NCÞ since theby ð SM;CC
N
N
N
N
rate of detectable events via the NC reaction by IceCube

103012-3

43

SHIGERU YOSHIDA

is proportional tothis case.

PHYSICAL REVIEW D 82, 103012 (2010)
−6

10

NC
N . We also show the constraint in

IceCube 2007
10EeV

In this analysis we use the IceCube observation resultswith 242 days data in 2007 to limit N using Eq. (5). No
detection of signal candidates in the measurement has led
to an upper limit of the neutrino ﬂux of 1:4 
106 GeV cm2 sec1 sr1 [7] in the energy range from3  107 to 3  109 GeV. The effective area Al is
0:7 km2 for , 0:4 km2 for , and 3  104 km2 for0 s [7]. Constraints on N are then derived with Eq. (5).
The results for Es ¼ 109 and 1010 GeV are shown in
Fig. 2. Enhancing the charged current cross section bymore than a factor of 30 for E ¼ 1 EeV (109 GeV) is
disfavored if the astrophysical neutrino intensities arearound107 GeV cm2 sec1 sr1 , near the upperbound of the GZK cosmogenic neutrino bulk. Note thatneutrino-nucleon
collision with E ¼ 1 EeV corresponds
pﬃﬃﬃ
to s 40 TeV and the present limit on N would placea rather strong constraint on scenarios with extra dimensions and strong gravity, although more accurate estimation requires studies with a model-dependent approach
which implements the cross section and the ﬁnal-stateparticles from the collision predicted by a given particle
physics model. Taking into account uncertainty on theastrophysical neutrino ﬂuxes, any model that increases
10−6

IceCube 20072

j (E) E [GeV cm−2 sec −1 sr −1]

10EeV

10−7

1EeV

10−8

10−9
10−33

10−32

10−31

10−30

10−29

σνN [cm ]2

FIG. 2 (color online). Constraints on the all-ﬂavor sum of
cosmic neutrino ﬂux and the charged current N cross section
based on the null detection of neutrino signals by the IceCube
2007 observation. The right upper region is excluded by thepresent analysis. The horizontal lines provide references of the
expected GZK cosmogenic neutrino ﬂuxes [20] and the verticallines correspond to the SM cross section [19].

j(E) E 2 [GeV cm −2 sec−1 sr−1]

B. Results

1EeV

10−8

10−9
10−33

10−32

10−31

10−30

10−29

σνN [cm2 ]FIG. 3 (color online). Constraints on the all-ﬂavor sum of
cosmic neutrino ﬂux and the neutral current N cross section
for the scenario that only the neutral current reaction is enhanced
by a new physics beyond the standard model. The right upper
region is excluded by the present analysis. The horizontal lines
provide references of the expected GZK cosmogenic neutrino
ﬂuxes [20] and the vertical lines correspond to the SM crosssection [19].

the neutrino-nucleon cross section to produce charged
pﬃﬃﬃ
leptons by more than 2 orders of magnitude at s
40 TeV is disfavored by the IceCube observation.
However, we should point out that the IceCube 2007 data
could not constrain the charged current cross section if theintensity of cosmic neutrinos in the relevant energy regionis fewer than 108 GeV cm2 sec1 sr1 , within thelower range of prediction for the cosmogenic neutrino
ﬂuxes [18]. Absorption effects in the Earth becomes sizable in this case, resulting in less sensitivity to the crosssection. This limitation will be improved for larger detection areas of the full IceCube detector.
Figure 3 shows the constraints when only the NC crosssection p
isﬃﬃﬃvaried. Enhancement of NC
N by a factor beyond
100 at s 40 TeV is disfavored, but this strongly depends on the cosmic neutrino ﬂux one assumes. Because
the NC interaction does not absorb neutrinos during theirpropagation though the Earth, the cross section could bebounded even in the case when the neutrino ﬂux is small,but the limit becomes rather weak; the allowed maximum
enhancement factor is on the order of 103 .
III. CONSTRAINT ON THE MICROSCOPIC
BLACK HOLE PRODUCTION
A constraint on a speciﬁc physics model that enhances
the neutrino-nucleon cross section is obtained by the same

103012-4

44

10−7

CONSTRAINTS ON NEUTRINO-NUCLEON INTERACTIONS . . .
6

GZK ν

PHYSICAL REVIEW D 82, 103012 (2010)

10

−7

10

−8

10

−9

10

−10

10

−11

10

−12

4

μ

2

τ
2

0
−1

−0.5

0

0.5

Downward

τ

−2

−1

dN/dE E [GeV cm sec ]Flux [10−18 cm−2 sec−1 sr−1]

E > 10PeV

1

10

Atm μ

μ

6

8

10

10

10

12

10

Energy [GeV]

cos (Zenith Angle)

FIG. 4 (color online). (Left) integral ﬂuxes of the muon and taus above 10 PeV ( ¼ 107 GeV) at IceCube depth ( 1450 m) of the
GZK cosmogenic neutrinos [17] in case of the microscopic black hole creation scenario [5] for ðMD ; xmin Þ ¼ ð1 TeV; 1Þ (solid line),(1 TeV,3) (dotted-dashed line). The dashed line corresponds to the intensities obtained by the SM N cross section [19]. (Right) energy
spectra of the GZK  induced muons and taus at IceCube depth with downgoing [i.e. cosðzenithÞ  0] geometry expected by the blackhole model for ðMD ; xmin Þ ¼ ð1 TeV; 1Þ. The spectra produced by the SM cross section are also shown as dashed lines for comparison.
The curve labeled ‘‘Atm ’’ represents the atmospheric muon intensity estimated by the IceCube observation with its uncertainty
expressed by the two dashed lines [21].

procedure for the model-independent bound, except thetransport equations, Eqs. (1) and (2), would have total
and differential neutrino cross section provided by both
SM and the new model. Here we study the model of blackhole creation as a possible consequence of low-scale gravity that may occur if space-time has more than four dimensions. We use the predicted cross section of lack hole
production via the neutrino-nucleon scattering describedby Ref. [5], parametrized by the Planck scale MD , the ratioof the minimal black hole mass to the Planck scale xmin ,and the space-time dimension D ¼ 4 þ n. In this papern ¼ 6 and MD ¼ 1 TeV are assumed as representative
numbers. The resultant cross section may exceed SMinteraction rates by 2 orders of magnitude or even greater.
Therefore, the model-independent bound shown in theprevious section indicated that the 2007 IceCube observation should be already sensitive to some of the parameter
space in the black hole creation model.
The ﬁnal states in the neutrino-nucleon scattering in thismodel are quite different from the SM case. Black holes
evaporate and generate multiple particles of all kinds,
like leptons, quarks, gluons, and bosons. These products
are distributed according to the number of degrees of
freedom. Consequently, the average number of muonsand taus, Nþ , are 1=30 of all particle average multi which is also determined by the speciﬁc model.
plicity N,
As N 10 at neutrino energy of E ¼ 1 EeV, multiple
muon or tau production would very rarely occur. Then theeffective differential cross section d N =dE; in the transport equations (1) and (2) in the black hole model isrepresented byd NNþ ðE Þ
¼
dE;
2

N ðE Þ

 Þ
NðE
2E

(6)

 We take N from Ref. [5] in thewith 0 E; 2E =N.
present calculation. In this speciﬁc scenario, a muon or atau carries a small fraction (1=N 0:1) of incoming neutrino energy E in average, in contrast to the SM collisionthat takes away 1  y 0:8 of neutrino energy by a generated charged lepton.
Solving the transport equations gives the intensities ofsecondary muons and taus, which are shown in Fig. 4. One
can ﬁnd in the zenith angle distribution (the left panel) thatthe intensities are increased by more than 2 orders ofmagnitude above the SM case. The large increase of Nenhances downgoing event rates while the upgoing muonand tau rates are more suppressed. The zenith angle distribution is consistent with the original work in Ref. [5]. It
should also be noted that the energy spectra is substantially
modiﬁed from those in the SM case (the right panel). The
peak energy is around 1 EeV, an order of magnitude lower
than the SM spectrum, reﬂecting the fact that a smaller
fraction of neutrino energy is channeled into muons andtaus via the black hole evaporation. The peak happens tomatch the most sensitive energy region in the IceCube EHE
neutrino search [7].
Because N is solely predicted by the speciﬁc model,
the model-dependent constraints on N interactions isrepresented in the plane of extraterrestrial neutrino ﬂux
and the number of events the IceCube 2007 run would
have detected. Figure 5 shows the number of events as afunction of the neutrino intensity at energy of 1 EeV, if the103012-5

45

SHIGERU YOSHIDA

j(E) E 2 [GeV cm−2 sec−1 sr−1]

10

PHYSICAL REVIEW D 82, 103012 (2010)−6

IV. CONCLUSIONS

10 −7

10 −8

10 −9
10 −2

10 −1

1

10

Number Of Events

FIG. 5 (color online). Number of events as a function of
extraterrestrial neutrino ﬂux at 1 EeV for ðMD ; xmin Þ ¼
ð1 TeV; 1Þ (solid line), (1 TeV,3) (dashed line). The 90% C.L.
line determined by the Poisson statistics is also shown as avertical line for reference.

The IceCube 2007 observation indicated that any
scenario to enhance either the NC or both the NCpﬃﬃandﬃ
CC equivalent cross section by more than 100 at s
40 TeV is unlikely if the sum of the all three ﬂavors ofastrophysical neutrino ﬂuxes are greater than3108 GeV cm2 sec1 sr1 in the EeV region. Many models of the GZK cosmogenic neutrinos exist to predict thisﬂux range, thus the present constraints limit new particle
physics beyond the SM, unless the extraterrestrial neutrino
intensity is smaller than the expectation. The example ofthe model-dependent bound on N has been also shownfor the microscopic black hole evaporation scenario. A
high cosmic neutrino intensity constrains the parameter
space of the black hole creation. Future observation by
the rapidly growing IceCube detectors will strongly limit
particle physics models which predict an increase ofneutrino-nucleon interaction probability.
ACKNOWLEDGMENTS

microscopic black hole evaporation occurs as in Ref. [5].
The Poisson statistics then determine the upper limit ofneutrino ﬂux that can be still consistent with the null
observation by IceCube. It is indicated that the neutrino
intensity of 107 GeV cm2 sec1 sr1 is disfavored in this
scenario. More parameter space of MD and xmin will befurther constrained by near future observation with
IceCube whose detection volume is rapidly growing withan increase of the number of detectors in operation.

We wish to acknowledge the IceCube Collaboration for
useful discussions and suggestions. We thank Jonathan
Feng for helpful discussions on the physics models beyond
the standard model and providing numerical data of thecross section and multiplicity distribution predicted by the
micro black hole creation scenario. We also wish to thankLisa Gerhardt for helpful comments on the manuscript.
This work was supported in part by the Grants-in-Aid in
Scientiﬁc Research from the JSPS (Japan Society for the
Promotion of Science) in Japan.

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PHYSICAL REVIEW D 82, 072003 (2010)

First search for extremely high energy cosmogenic neutrinos
with the IceCube Neutrino Observatory
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D. Z. Besson,26 M. Bissok,1 E. Blaufuss,17 D. J. Boersma,1 C. Bohm,34 S. Böser,11 O. Botner,37 L. Bradley,36 J. Braun,28
S. Buitink,8 M. Carson,22 D. Chirkin,28 B. Christy,17 J. Clem,31 F. Clevermann,20 S. Cohen,25 C. Colnard,23
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F. Descamps,22 P. Desiati,28 G. de Vries-Uiterweerd,22 T. DeYoung,36 J. C. Dı́az-Vélez,28 J. Dreyer,10 J. P. Dumm,28
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A. R. Fazely,6 T. Feusels,22 K. Filimonov,7 C. Finley,34 M. M. Foerster,36 B. D. Fox,36 A. Franckowiak,11 R. Franke,40
T. K. Gaisser,31 J. Gallagher,27 R. Ganugapati,28 M. Geisler,1 L. Gerhardt,8,7 L. Gladstone,28 T. Glüsenkamp,1
A. Goldschmidt,8 J. A. Goodman,17 D. Grant,21 T. Griesel,29 A. Groß,16,23 S. Grullon,28 M. Gurtner,39 C. Ha,36
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S. Odrowski,23 A. Olivas,17 M. Olivo,37,10 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,39 P. B. Price,7 M. Prikockis,36 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 C. Roucelle,23
T. Ruhe,20 D. Rutledge,36 B. Ruzybayev,31 D. Ryckbosch,22 H.-G. Sander,29 S. Sarkar,32 K. Schatto,29 S. Schlenstedt,40
T. Schmidt,17 D. Schneider,28 A. Schukraft,1 A. Schultes,39 O. Schulz,23 M. Schunck,1 D. Seckel,31 B. Semburg,39
S. H. Seo,34 Y. Sestayo,23 S. Seunarine,12 A. Silvestri,24 A. Slipak,36 G. M. Spiczak,33 C. Spiering,40 M. Stamatikos,18,kT. Stanev,31 G. Stephens,36 T. Stezelberger,8 R. G. Stokstad,8 S. Stoyanov,31 E. A. Strahler,14 T. Straszheim,17
G. W. Sullivan,17 Q. Swillens,13 I. Taboada,5 A. Tamburro,33 O. Tarasova,40 A. Tepe,5 S. Ter-Antonyan,6 S. Tilav,31
P. A. Toale,36 D. Tosi,40 D. Turčan,17 N. van Eijndhoven,14 J. Vandenbroucke,7 A. Van Overloop,22 J. van Santen,9B. Voigt,40 C. Walck,34 T. Waldenmaier,9 M. Wallraff,1 M. Walter,40 C. Wendt,28 S. Westerhoff,28 N. Whitehorn,28
K. Wiebe,29 C. H. Wiebusch,1 G. Wikström,34 D. R. Williams,2 R. Wischnewski,40 H. Wissing,17 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, Clark-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 and 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= 2010=82(7)=072003(11)072003-1

Ó 2010 The American Physical Society47

R. ABBASI et al.

PHYSICAL REVIEW D 82, 072003 (2010)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 Subatomic and Radiation Physics, 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, United Kingdom
33
Department of Physics, University of Wisconsin, River Falls, Wisconsin 54022, USA
34
Oskar Klein Centre 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 and Astronomy, Utrecht University/SRON, NL-3584 CC Utrecht, The Netherlands
39
Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
40
DESY, D-15735 Zeuthen, Germany(Received 7 July 2010; published 7 October 2010)
We report on the results of the search for extremely-high energy neutrinos with energies above 107 GeV
obtained with the partially ( 30%) constructed IceCube in 2007. From the absence of signal events inthe sample of 242.1 days of effective live time, we derive a 90% C.L. model independent differential upper
limit based on the number of signal events per energy decade at E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 for neutrinos in the energy range from 3  107 to 3  109 GeV.
DOI: 10.1103/PhysRevD.82.072003

PACS numbers: 98.70.Sa, 95.85.Ry

I. INTRODUCTION
Detection of extremely-high energy (EHE) neutrinos
with energies greater than 107 GeV may shed light on
the long standing puzzle of the origin of EHE cosmic
rays [1,2]. Several observational results have indicatedthat these EHE cosmic rays (EHECRs) are of extragalactic
origin [3]. Further elucidation of their production mechanism by EHECR observation is, however, limited because
the collisions of EHECR with the cosmic microwave background photons—known as the Greisen-Zatsepin-Kuzmin(GZK) mechanism [4]—prevent EHECRs from propagating over cosmological distances without losing a sizable*Corresponding author.
aya@hepburn.s.chiba-u.ac.jp†
Also at Universität Erlangen-Nürnberg, Physikalisches
Institut, D-91058, Erlangen, Germany.
‡
Corresponding author.
mase@hepburn.s.chiba-u.ac.jp
xAlso at Università di Bari and Sezione INFN, Dipartimento di
Fisica, I-70126, Bari, Italy.
k
Also at NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA.
{
Corresponding author.
syoshida@hepburn.s.chiba-u.ac.jp

fraction of their energy. On the other hand, cosmogenic
neutrinos [5] produced by the GZK mechanism via photoproduced  meson decay as  !   ! e e 
carry information on the EHECR source evolution andthe maximum energy of EHECRs at their production
sites [6].
Detection of these EHE neutrinos is an experimental
challenge because the very low EHE neutrino ﬂuxes require a very large detector. The large size of the IceCube
neutrino observatory [7], currently under construction at
the geographic South Pole, will make it more effective thanprevious experiments in the search for these neutrinos[8,9]. Interactions of  , e , and  and their antiparticles
are observed through the Cherenkov radiation emitted
by secondary particles. In the following, we do not distinguish between  and ; the simulations and sensitivity
calculations assume an equal mixture of particles andantiparticles.
In this paper we will describe the ﬁrst results of a searchfor signatures of cosmogenic neutrinos in the 2007 dataacquired by the partially constructed IceCube neutrino
observatory. This analysis selects events which produce alarge amount of light in the detector. Based on simple
criteria, such as the total number of observed Cherenkov

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photons and the results of reconstruction algorithms, it
selects candidate neutrino events. Although  , e , and interactions look very different in IceCube, the selection
criteria are sensitive to all three ﬂavors.
II. THE ICECUBE DETECTOR
IceCube is a cubic-kilometer, high-energy cosmic neutrino telescope which is currently under construction. It
uses the 2800 m thick glacial ice as a Cherenkov medium.
Cherenkov photons emitted by relativistic charged particles, notably muons, electrons, and taus produced incharged current interactions and their secondaries, aredetected by an array of photon sensors, known as digital
optical modules (DOMs) [10]. The DOMs deep below theice surface are deployed along electrical cable bundles thatcarry power and communication between the DOMs andsurface electronics. The cable assemblies, often called
strings, are lowered into holes drilled to a depth of
2450 m. The DOMs, spaced at intervals of 17 m, occupy
the bottom 1000 m of each string. The strings are arranged
in a hexagonal lattice pattern with a spacing of approximately 125 m. DOMs are also frozen into tanks located at
the surface near the top of each hole. The tanks constitutean air shower array called IceTop [11].
The DOMs enclose a down-looking 25 cm photomultiplier tube (PMT) [12] with data acquisition and calibrationelectronics, light emitting diodes for calibration, and also
data compression, communications, and control hardware[10] in a 35 cm diameter pressure sphere. Almost all of the
PMTs are run at a gain of 107 ; PMT saturation effects
become important at signal levels of about 5000 photoelectrons in a single DOM in 50 ns. When the DOM detects
a photoelectron, it initiates an acquisition cycle, recording
the PMT output with two waveform digitizer systems. The
ﬁrst system samples every 3.3 ns for 400 ns, with 14 bits ofdynamic range. The second system samples every 25 ns for
6:4 s, with 10 bits of dynamic range. The data acquisition
system is designed such that the ﬁrst system is sensitive to abright photon source at close distance and the second
system captures signal induced by photons emitted at large
distance. This analysis uses the total number of photoelectrons detected by the PMTs as a measure of the event
energy. For each DOM, the charge used is the one fromwhichever system recorded a larger number of photoelectrons. Because of the signiﬁcant DOM-to-DOM differences in saturation behavior, the current analysis does not
attempt to correct for PMT saturation. So, the signals frombrightly illuminated DOMs are naturally truncated.
III. DATA AND SIMULATIONThis analysis uses data collected from May 2007
through April 2008, when IceCube consisted of 22 strings(IC-22; 1320 DOMs) and 52 IceTop tanks. In order togreatly reduce random noise from radioactivity, in IC22

the DOMs only recorded signal waveforms when a local
coincidence condition was satisﬁed, i.e. when an adjoiningor next-to-nearest neighbor DOM was triggered within1 s. In 2007, the trigger selected time periods when 8
or more DOMs recorded local coincidence signals within
5 s; when this happened, all hits within a 20 s window
were stored as an event. The average trigger rate was about
550 Hz. The high-multiplicity event sample used in thisanalysis imposes an additional condition requiring NDOM
 80, where NDOM is the number of hit DOMs in an
event. The average high-multiplicity event rate was approximately 1.5 Hz with a seasonal variation of 17%. A
total of 3:2  107 events were tagged as high-multiplicity
during the effective live time of 242.1 days (excluding theperiods of unstable operation).
The high-multiplicity cut reduces the data by a factor of3  103 while preserving approximately 70% of the
GZK neutrinos with projected trajectories that pass within
880 m of the center of IceCube. Here, and below, the GZK
signal rates are based on the GZK spectra and ﬂux calculated by Ref. [6] assuming an all-proton composition witha moderately strong source evolution, ðz þ 1Þm with m ¼ 4extending to z ¼ 4:0. Neutrino oscillations modify theneutrino ﬂavor ratio over the cosmological distances they
travel and the ﬂuxes at the Earth were calculated as inRef. [13]. Note that the ﬂavor ratio e : : of cosmogenic neutrinos at the Earth is different from 1:1:1 asprimary energy spectra of e and  produced by the
GZK mechanism are different because of a signiﬁcant
contribution of e from neutron decay. This enhancement
was included in the GZK neutrino ﬂux calculations
used here.
EHE neutrinos were simulated with the JULIET package[9] to generate and propagate the neutrinos through the
Earth. All three ﬂavors of neutrinos were simulated withenergies between 105 and 1011 GeV. The resulting secondary muons and taus produced in the neutrino interactions
are propagated through the rock and ice near the IceCube
volume, also by JULIET. Hadronic and electromagnetic
showers are also simulated; all of these showers are treatedas point sources, without accounting for the LPM effect.
The background muon bundles from cosmic rays in theenergy range 106 to 1010 GeV were generated using
CORSIKA [14] version 6.720 with the SIBYLL 2.1 hadronicinteraction model or with QGSJET-II, without charm production [15]. The uncertain prompt muon component fromcharm decay may contribute to the background events [16].
The muons were propagated through the Earth using MMC[17]. Departures of observed data distributions from thoseof the CORSIKA based background events prompted us toalso develop a phenomenological background model basedon ﬁts to data. Emission of Cherenkov photons and theirpropagation in the ice was simulated by the Photonics
package [18]. Measurement of the absolute number of
Cherenkov photons is important in the EHE neutrino

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7.5

search as it closely relates to the energy of the high-energymuons, taus, or electrons produced by EHE neutrinos.
Therefore, the detection efﬁciency of the DOMs must be
understood with good precision. The primary element, thePMT, is calibrated in the laboratory using a nitrogen laser
to measure the photon detection efﬁciency [12]. This bare
PMT data are used in a simulation package which propagates photons inside the glass sphere and the optical gel tothe photocathode surface. The DOM simulation is followed by waveform calibration and the trigger condition
is included in the simulation chain.

7

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IV. ANALYSIS

3.5

A. Extremely-high energy event signatures
and the initial event ﬁlter

6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11
log (in-ice energy/GeV)

0

10

The event signatures from  , e , and  are very different. IceCube mainly detects cosmogenic neutrinos by thesignals from the secondary muons and taus generated in theneutrino interaction in the rock or ice. At high energies,
these particles are seen in the detector as series of energetic
cascades from radiative energy loss processes such as paircreation, bremsstrahlung, and photonuclear interactions,rather than minimum-ionizing tracks. The radiative energy
losses are approximately proportional to the energy of themuon or the tau, and so is the Cherenkov light yield.
Electron neutrinos produce electromagnetic and hadronic
showers, which are relatively compact sources of
Cherenkov light. Muon and tau neutrinos within IceCube
will also produce a hadronic shower from the struck nucleon, in addition to the muon or tau secondary.
Shown in Fig. 1 is the simulated distribution of the total
number of photoelectrons per event (NPE) recorded by thethe IC-22 detector as a function of the simulated true muonenergy. A clear correlation between NPE and the energy ofparticles measured near IceCube is observed. The energies
are sampled at a radius of 880 m from the IceCube center.
This deﬁnition of energy is labeled ‘‘in-ice energy’’ andused throughout this paper. The visible departure fromlinearity for large NPE stems from the saturation of thedetector during signal capture. Approximately 30% of
EHE signal events are due to neutrino interactions inside
the IceCube detector volume initiating a hadronic or electromagnetic cascade. The correlation between NPE andincoming neutrino energy also holds for these events.
Electron neutrinos are detectable via this channel.
Because the energy spectrum of background atmospheric muons (both single muons and bundles) falls steeply
with energy, the GZK neutrino ﬂux should dominate overbackground in the high NPE region. Since the throughgoing muons and taus induced by EHE neutrinos enter into
the IceCube volume mainly horizontally [8,9], the signal
search criteria are chosen to favor roughly horizontal highNPE events.
The high-multiplicity NDOM  80 sample is dominatedby atmospheric background muons. The next step of the

FIG. 1 (color online). Event distribution from Monte Carlosimulations of single muons with the IC-22 detector conﬁgurations in a plane of NPE and simulated true energy. The muonenergy is given when the muon is 880 meters from the IceCube
center (in-ice energy). The 80 DOM multiplicity cut (level-1 cut)is applied. The charged lepton energy distribution is assumed tofollow E1 in this plot for illustrative purposes. Only particles
with trajectories intersecting within 880 m from the center of
IceCube array are considered in the plots. More distant events do
not contribute to the data sample.

analysis selects events with NPE > 104 . This reduces the
background by 3 orders of magnitude, leaving 6528 events,
still dominated by background, while the GZK signal
reduction is 24%.
Table I summarizes the number of events remaining at
each level of the initial ﬁltering. In order to estimate thebackground in the very high-energy region, the simulated
data are compared to the experimental data in the region
104 < NPE < 105 . The present analysis follows the blind
analysis technique. In keeping with the IceCube blindness
policy, events with NPE  105 were not used for determining the background or setting cuts. This NPE threshold waschosen so that the possible contribution from signal eventsin the studied sample was negligible.
B. High-energy muon background
Bundles of muons generated in cosmic-ray air showers
are the major background for the EHE neutrino signal
search, because multiple muon tracks with a small geometrical separation resemble a single high-energy muon in
the IceCube detector. The multiplicity, energy distribution,and separation distances for these muon bundles are notfully understood. Two independent Monte Carlo simulations are carried out to estimate the muon-bundle background in this EHE neutrino signal search.
The ﬁrst is the full cosmic-ray air shower simulation
with light and heavy ion primaries using the CORSIKA(SIBYLL) package [14]. Two extreme cases of composition
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TABLE I. Number of events at different ﬁlter levels for 242.1 days in 2007. The simulation predictions for the atmospheric muon
background using the CORSIKA-SIBYLL package, the empirical model, and that for the GZK cosmogenic neutrino model are also listed
for comparison. Errors shown here are statistical only. Refer to Sec. IVA for the deﬁnitions.
Filter levels

Observational data

Level 1 (NDOM  80)
Level 2 (NPE > 104 )3:195  107
6528

CORSIKA (iron)Empirical model

uncertainty in the primary cosmic-ray mass population.
While the full air shower simulation includes a calculationof the production spectra of the multiple muons frommeson decay, the simulation still introduces a large uncertainty because both the primary composition at relevant
cosmic-ray energies (> 107 GeV) and the hadronic interaction model are highly uncertain.
The second simulation uses a model relying on a phenomenological ﬁt to part of the experimental high-energy
data. This empirical model approximates multiple muontracks in an event by a single high-energy muon which isadequate at very high energies for the variables used in thisanalysis. The single muon approximation predicts larger
ﬂuctuations in NPE due to radiative energy losses ofenergetic muons, giving a rather conservative estimateof the background passing rate. The two independent setsof simulations with top-down and bottom-up approaches
to describe the observational data complement each otherimproving the reliability of the background estimation.
1. Background estimation with CORSIKA
Figure 2 shows distributions for data and simulations at
level-2 for NPE, the reconstructed zenith angle (), and thecenter-of-gravity depth of the events (zCOG ). The CORSIKA
NPE distribution is extrapolated to the higher NPE region.
Extrapolation was necessary mainly because of a lack ofsimulated CORSIKA events at primary cosmic-ray energies
above 1010 GeV. The extrapolation accounts for the observed GZK cutoff at an energy around 5  1019 eV. The
NPE-weighted LineFit algorithm was used to reconstruct

2. Construction of an empirical model
The empirical model is optimized to match the level-2
experimental data (104 < NPE < 105 ). The possible signal

10 2
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5

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10

Number of events in 242 days

Number of events in 242 days

Number of events in 242 days

104

10 3

4

Signal (GZK1 [6])zenith angle in this initial study. The NPE-weighted
LineFit is a simple minimization of 2 ¼ i NPEi ðr~i ~ 2 , where ti and NPEi represent, respectively,
r~COG  ti vÞ
the time of the ﬁrst photoelectron and the number ofphotoelectrons recorded by the ith DOM at the positioni xi i NPEi yi i NPEi zi
r~i and r~COG  ði NPE; i NPEi ; i NPEi Þ is the NPEi NPEi
weighted position of the center of gravity of the hits. The
ﬁt ignores the geometry of the Cherenkov cone and theoptical properties of the medium and assumes light traveling with a velocity v~ along a one-dimensional path throughthe detector, passing through the center of gravity.
The measured event rates are close to the simulated rates
based on CORSIKA-SIBYLL with iron primaries and above
those based on CORSIKA-SIBYLL proton data in most regions. A signiﬁcant discrepancy can be found in the rate ofevents with cos 0:3, i.e. events reconstructed as horizontal or up-going, which is largely underestimated.
Replacing SIBYLL with other hadronization models (e.g.
QGSJET-II) does not change this behavior. The discrepancy
may be due to a combination of uncertainties in the hadronic interaction models, cosmic-ray ﬂux, and Cherenkov
photon propagation in the glacial ice. Since the horizon is
the key region for the EHE neutrino search, the backgroundestimations were supplemented by an empirical model ﬁt
to a subsample of the data.

10 4

10-1

CORSIKA (proton)ð1:84  0:08Þ  107 ð7:71  0:45Þ  106 ð886  8:9Þ  103
ð6:82  0:42Þ  103 ð1:09  0:09Þ  104 ð1:63  0:17Þ  103 ð670  7:5Þ  103

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1

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-400 -200

0

200

400

zCOG [m]FIG. 2 (color online). Event distributions for NPE, cosine of reconstructed zenith angle, and the NPE-weighted mean depth ofevent (zCOG ) for observational and the background Monte Carlo simulation data. The black dots represent observational data after the
NPE > 104 cut, red for CORSIKA proton (SIBYLL), magenta for CORSIKA iron (SIBYLL). Green shaded regions represent distributions
obtained with the empirical model with the size of shade expressing the uncertainty of the model. See text for the details.

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R. ABBASI et al.

4.5

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6

log10(Total NPE)

-400 -2000

200 400zCOG [m]FIG. 3 (color online). Event distributions from the level-3 samples as functions of NPE (left) and zCOG (right). The black dots
represent observational data, green boxes represent the empirical model including uncertainty. Red and magenta lines are CORSIKA
samples with SIBYLL interaction model and proton and iron primaries, respectively. The left panel also includes the expected NPE
distribution of events induced by the cosmogenic neutrinos [6] shown by the blue line for reference.

region (NPE  105 ) is not used to avoid bias. The model
provides a relation between the NPE of an event and thecosmic-ray primary energy. Its convolution with thecosmic-ray ﬂux then gives the event rate with a given
NPE. The cosmic-ray ﬂux used in the present analysis istaken from the compilation in Ref. [2].
The model is based on the so-called Elbert formula [19]which parametrizes the mean multiplicity of muons withenergies above a certain threshold E :

 

AE
E A2 AE 1
;N ¼ TE0 cos0 E0
E0(1)
ET ¼ 14:5 GeV;
where A, E0 , and 0 are the mass number, the energy, andthe zenith angle of the primary cosmic ray [20]. The energy
weighted integration of the formula relates the total energy
carried by a muon-bundle EB to the primary cosmic-ray
energy E0 ,  þ1
Z E0 =A dN
AA
E dE ’ ET
;
EB 
dE
cos0  1 E0
(2)
1. Here, is empirically determinedassuming AE =E0
by ﬁt to the observed data. Assuming its corresponding
energy at the IceCube depth, in-ice , is independent ofzenith angle, (and thereby EB ) can be calculated as afunction of zenith angle by taking into account the energy
loss during propagation through the Earth. The optimization of the two parameters and in-ice is performed bycomparing the observed data to simulation of a single highenergy muon with energy of EB in the NPE and zenith
angle space, independently. A ¼ 1 is assumed in the optimization. The event distributions derived from the empirical model with optimized parameters ( ¼ 1:97 andin-ice¼ 1500 GeV) are given in Fig. 2. The green shaded
region in the plot is obtained by allowing the model parameters to vary within 1 from their optimized values.

The discrepancies of zCOG at large depths for the empiricalmodel and at small depths for CORSIKA/iron seem to be due
to vertical, down-going events because a restriction of thezenith angle, cos < 0:8, improves the agreement in bothcases. Since the majority of the EHE neutrino induced
events is close to the horizon we can discard all eventswith cos < 0:8 without signiﬁcant loss of signal efﬁciency (level-3 cut). The resulting distributions are shownin Fig. 3.
C. Search for EHE cosmogenic neutrino signal
The level-4 cut to eliminate the muon background is
carried out in the NPE- cos (NZ) plane. In accordancewith the requirements of blindness, the cuts are ﬁnalized on
simulated events alone without referring to real data.
Because the optical properties of the glacial ice vary signiﬁcantly with depth [21], and because the changing absorption and scattering lengths affect what IceCube
observes, the ﬁnal cuts are chosen to be depth dependent.
The cuts are chosen based on the depth of the weighted
center of gravity of the event, zCOG . The distribution of
events in the NZ plane depends on zCOG . We divide theevents into two groups according to their zCOG as follows:
region A:  250 < zCOG < 50 m
zCOG > 50 m;

region B: zCOG < 250 m

and 50 < zCOG < 50 m:
As seen in Fig. 4, region B contains a large number ofhorizontal and up-going mis-reconstructed background
events, whereas the fraction of such events in region A is

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-0.6

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-0.6

10-4

-0.6

-0.8

10-5

-0.8

10-5

-0.8

10-6

-1

10-6

-1

5.5

6

6.5

4

4.5

log (NPE)

5

5.5

6

6.5

10

10-3

10-4

-0.6

10-4

10-5

-0.8

10-6

-1
4

10-5

4.5

5

5.5

6

6.5

10-6

log (NPE)
10

104

0.8

103

0.8

103

0.6

102

0.6

102

0.4

10

0.4

10

0.2

1

0.2

1

0

10-1

0

10-1

-0.2

10-2

-0.2

10-2

-0.4

10-3

-0.4

10-3

10-4

-0.6

10-4

-0.6

10-4

-0.8

10-5

-0.8

10-5

-0.8

10-5

-1

10-6

-1
4

10-6

-1

0.8

103

0.8

103

0.6

102

0.6

102

0.4

10

0.4

10

0.2

1

0.2

1

0

10-1

0

10-1

-0.2

10-2

-0.2

10-2

-0.4

10-3

-0.4

10-3

-0.6

10-4

-0.6

-0.8

10-5

-1
4

10-6

cos(zenith angle)

6.5

10-2

-0.4

1

104

6.5

6

-0.2

Region B: Background MC (CORSIKA)
104
1

1

6

5.5

10-1

10

Region B: Background MC (empirical)
104

5.5

5

1

0

log (NPE)

10Region B: Experimental data (2007)5

4.5

log (NPE)

1

4.5

4

0.2

4

4.5

log (NPE)

5

5.5

6

6.5

log (NPE)

10

4.5

5

5.5

6

6.5

Region B: GZK signal MCcos(zenith angle)

5cos(zenith angle)

4.5

Region A: GZK signal MCcos(zenith angle)

104

cos(zenith angle)

1

Region A: Background MC (CORSIKA)
104
1

-1
4

cos(zenith angle)

PHYSICAL REVIEW D 82, 072003 (2010)

Region A: Background MC (empirical)cos(zenith angle)

cos(zenith angle)

Region A: Experimental data (2007)

44.5

log (NPE)

10

5

5.5

6

6.5

10-6

log (NPE)
1010FIG. 4 (color online). Event number distributions passing the level-2 selection cut (NPE > 104 ) of the experimental data (left), thebackground from the empirical model (middle left), the background from CORSIKA-SIBYLL with iron primaries (middle right), and thesignal (right) on the NZ plane at the IceCube depth. The upper (lower) panels show the distributions in the region A (B). The GZK
neutrino ﬂux [6] determines the event intensity in the signal Monte Carlo plot, adding all three ﬂavors of neutrinos. The series of thicklines in each panel indicates the level-3 ( cosðÞ < 0:8) and the ﬁnal level-4 cuts.

very small. Figure 4 also shows the distributions of theexperimental data and the simulated GZK neutrino induced
signal events. The latter clearly accumulate near the horizontal direction regardless of the zCOG position and have on
average larger NPE than the background sample. The
selection criteria to separate signal from background aredetermined for region A and region B separately: For eachbin of cos (width 0.1), a threshold NPE is set such that the
number of background events above the threshold is lessthan 104 . Tighter cuts to further reduce the backgroundwould also reduce the signal to an undesirable degree. The
NPE thresholds in all the zenith angle bins are then connected to each other to form a series of lines on the NZ
plane, deﬁning the ﬁnal level-4 cut, as drawn in Fig. 4. The
cuts were optimized using the empirical model for background simulations, so we used extrapolated CORSIKA/irondata as a check of the ﬁnal background level. Figure 4 also
shows the distribution of background events in the NZ
plane from the extrapolation. Table II summarizes thenumber of events remaining in the analysis after each of
the cut levels.
The effective area as a function of energy at Earth’s
surface for each neutrino ﬂavor is shown in the left panelof Fig. 5, averaged over all solid angles. The area increases with the energy owing to the increasing neutrino
interaction cross sections and the increased probability ofobserving the interactions, which is different for each
ﬂavor.
At low energies, most of the  signal comes from events
where the  interacts in the detector, or the  decays in it.
At higher energies,  energy loss becomes large enoughthat through-going taus also pass the cuts. Contributions
from  and  dominate over e in the energy range
above 108 GeV, as the secondary produced muons andtaus can travel long distances to reach the detection volume. This trend is reversed at lower energy where tau andmuon energy losses are smaller, and e ’s can deposit all of
their energy into the detector volume. The effective area

TABLE II. Number of events at analysis ﬁlter levels for 242.1 days in 2007. The simulation predictions for the atmospheric muon
background using the CORSIKA-SIBYLL package, the empirical model, and that for the GZK cosmogenic neutrino model are also listed
for comparison. Errors shown here are statistical only. See Secs. IV B and IV C for details.
Analysis ﬁlter levels
Level 3 ( cosðÞ < 0:8)
Level 4 (EHE  search)

Observational data
2014
0

CORSIKA (iron)Empirical model

CORSIKA (proton)

Signal (GZK1 [6])ð620  7:3Þ  103
ð6:32  1:37Þ  104 ð4:18  1:29Þ  104 ð1:44  0:58Þ  104 ð155  1:4Þ  103
ð2:65  0:21Þ  103

ð2:68  0:19Þ  103

ð4:16  0:40Þ  102

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103

10

PHYSICAL REVIEW D 82, 072003 (2010)

νe
νμ
ντ

1

Effective area [km2]

Effective area [m2]

104

2

10

−1

10

10−2
10−3

μ
τ
νe
νμ
ντ

10−4
10−5

1
6 6.5 7 7.5 8 8.5 9 9.5 1010.5

log 10 (Energy/GeV)

10−6

6 6.5 7 7.5 8 8.5 9 9.5 1010.5

log10(in−ice energy/GeV)

FIG. 5 (color online). The effective area of IC-22 for EHE
neutrino search. The left panel shows the 4 solid angle averaged area as a function of neutrino energy at the Earth surface.
The right panel shows the corresponding effective area forparticles at 880 m from the IceCube center entering into theIC-22 ﬁducial volume. Muons and taus in this plot are secondary
particles produced by neutrinos before reaching the neighborhood of the detector array. The energy here are deﬁned as in-ice
energy.

for  is larger than that for  at low energies, because of
the events where taus decay inside the detector. At thehighest energies, because of the larger mass of taus andincrease of the tau decay time with energy, the tau range islonger than that of muons, leading to a larger effective area.
The right panel in Fig. 5 shows the effective area as afunction of the in-ice energy (’’in-ice area’’). It represents
the probability of detection of incoming particles with thepresent analysis. The area for incident muons and taus
gradually increases with energy but is limited essentiallyby the physical cross section of the IC-22 array, 0:5 km2 .
Because the Cherenkov yield of taus is smaller than muons
with the same energy due to the smaller radiative energy
loss, the detection probability of incident taus is lower,
leading to the smaller in-ice area. Incoming neutrinos must
interact to yield Cherenkov light to be detected. Therefore,
the neutrino effective area becomes much smaller than thatfor muons or taus.
TABLE III. Expected event numbers passing the ﬁnal level-4
selection criteria in the 2007 IC-22 observation. Models include
the GZK models [6,22,23] and the Z-burst model [24]. The
predictions are normalized to a live time of 242.1 days. Signal
event numbers represent the sum over all three neutrino ﬂavors.
The ﬁrst uncertainty is the statistical uncertainty determined bysignal simulation statistics, and the second is the total systematic
uncertainty from sources discussed in Sec. V.
ModelsGZK1 [6]GZK2 [22]GZK3 [23]Z-burst [24]Number of Events per 242.1 days
3
ð155  1:4þ24
40 Þ  10
3ð248  2:3þ39
Þ

10
þ65
þ13
ð83  0:8þ21 Þ  103
3
ð398  3:4þ63
95 Þ  10

The expected number of signal events for various neutrino production models after the level-4 cut are summarized in TABLE III. GZK1 [6] represents the case of amoderately strong source evolution, ðz þ 1Þm with m ¼ 4extending to z ¼ 4:0, while GZK2 [22] assumes m ¼ 5 up
to z ¼ 2:0, and GZK3 [23] uses m ¼ 3 with a slightly
different parametrization and a cutoff structure.
V. THE SYSTEMATICSThis search is based on the eventwise NPE and reconstructed zenith angle. The main systematic uncertainties
derive from (1) the necessity to extrapolate the empiricalﬁt to data by approximately an order of magnitude in NPE
to estimate the background rate at the highest energies andfrom (2) the uncertainty of the absolute NPE scale. Table IVlists the sources of statistical and systematics errors.
A. Uncertainties in the background rate estimation
The largest uncertainty in the background rate estimate
arises from the fact that the parameters of the empiricalmodel were optimized for the observed events with 104 <NPE < 105 after level 2 selection. The limited statistics ofthis sample results in uncertainties on the parameters. The
model was then extrapolated to a higher NPE region for thedetermination of the level-4 cut.
Allowing the parameters to vary within 1 changes
the background rate by between 59% (for the softest
possible NPE spectrum after the level-4 cuts) and þ99%(for the hardest possible NPE spectrum). Uncertainties inthe detector sensitivity are incorporated by the parametrization. The difference in the background level estimatedwith the extrapolated CORSIKA/iron and the empiricalmodel can be taken to indicate the level of systematic
uncertainty due to model dependence. This uncertainty isapproximately 15% and can be assumed to include thepossible contribution from charm decay. An uncertainty
associated with the high-energy hadronic interaction
model is evaluated using simulated muon-bundle intensityfrom SIBYLL and QGSJET-II with iron primaries and found tobe 4%, which is negligible. An additional uncertainty of
17% arises from the seasonal variation of the atmospheric muon rate as the signal selection criteria are based
upon the season-averaged data.
B. Uncertainties of the signal rate estimate
The uncertainty in the relationship between measured
NPE and the energies of charged particles is the largest
systematic error affecting the signal event rate. It is theconsequence of our limited understanding of the detector
sensitivity, the photon propagation in ice, and the detector
response to bright signals. It is evaluated using absolutely
calibrated in situ light sources and amounts to a possible
overestimation of NPE in simulation by 18.5%, whichleads to decrease of the GZK signal rate by 21%.

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PHYSICAL REVIEW D 82, 072003 (2010)

TABLE IV. List of the statistical and systematic errors. The signal rate is estimated byassuming the high evolution ﬂux ðm; Zmax Þ ¼ ð4; 4Þ in Ref [6].

Statistical error
Detector sensitivity
Yearly variation
Empirical model
Background model dep.
NPE yield
Neutrino cross section
Photonuclear interaction
LPM effect
Total

Background rate

Signal (GZK) rate

22%

17%
þ99=  59%
15%




22% (stat.)þ102=  63% (sys.)

0:9%
8%



þ0=  21%
9%
þ10%
1%
0:9% (stat.)þ16=  26% (sys.)

Uncertainties of the relevant particle interactions in the
EHE regime also add systematics in the signal rate estimation. The expected event rate scales nearly linearly with
the neutrino-nucleon inelastic cross section in the EHE
range. This scaling has been conﬁrmed by numerical studies, artiﬁcially increasing the cross section. The crosssection uncertainty has been recently reduced to be around9% with the inclusion of the most recent data from
HERA and modern parton distribution functions [25].
Another systematic error arises from the photonuclear
cross section of EHE muons and taus. The present calculation used the model by Bugaev and Shlepin [26], rewritten in Ref. [27], that includes a relatively reliable soft
nonperturbative component and a less certain hard perturbative part. Ignoring the hard component in the simulation
gives the most conservative estimate of the uncertainty andleads to a 10% event rate increase. The suppression ofbremsstrahlung and pair production due to the LPM effect[28], for the relevant electron energies of 10910 GeV,
increases the effective radiation length of the electromagnetic cascade to Oð30–100Þ m from 36 cm [29]. Because
the value is still comparable to the IceCube DOM separation, and the contribution from e constitutes 20% of thetotal event rate in this energy range, the LPM effect has anegligible impact on the event rate. This has been conﬁrmed by a special simulation study on e including theLPM cascade elongation.

width of a decade of energy with condition that energy
dependence of neutrino ﬂux multiplied by the effective
area behaves as 1=E [31]. This limit is presented inFig. 6 including the systematic errors. The plot indicatesthat the EHE neutrino search by the IceCube observatory ismost sensitive to the neutrinos with energies on Earth’s
surface ranging between about 108 and 109 GeV. The
absence of signal events in the sample of 242.1 days ofeffective live time results in a 90% C.L. differential upper
limit on the neutrino ﬂux of E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 on average for neutrinos with
−4
10−
4

10−5

E2 φ(E) [GeV cm−2 sec−1 sr−1]

Error source

−6
10−6

differential upper limits

10−7

−8
10−8

IceCube−22
RICE
Auger
ANITA
AMANDA−II

neutrino models

GZK1
GZK2
GZK3
Z−burst

10−9

−10
−10
10

7

8

9

10

11

log (Energy/GeV)

VI. RESULTS

10

No events are observed in the ﬁnal data sample taken in2007 with a live time of 242.1 days when applying the ﬁnal
level-4 selection criteria, which is consistent with the expected number of background events of 6:3  104 . We
choose to present the resulting all ﬂavor EHE neutrino
upper limit in the quasi-differential form independent of
the neutrino production model. Assuming full mixing due
to oscillations, the experimental 90% conﬁdence level
upper limit is obtained by setting 2.44 events [30] for an
upper bound of the number of events observed with bin

FIG. 6. The all ﬂavor neutrino ﬂux differential limit from theIC-22 EHE analysis (ﬁlled circles). The systematic errors areincluded. Also the various model predictions are shown forcomparison: GZK model 1 [6] (short dashed line), GZK model
2 [22] (dotted line), GZK model 3 [23] (long dashed line),
Z-burst model [24] (dashed dot line). The model independent
differential upper limits by other experiments are also shown forAuger [32] (open triangles), RICE [31] (crosses), ANITA [34](open squares), AMANDA [35] (rhombi). Limits from otherexperiments are converted to the all ﬂavor limit assuming fullmixing neutrino oscillations and 90% C.L when necessary.

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PHYSICAL REVIEW D 82, 072003 (2010)

an energy of 3  107 E 3  109 GeV. Heree þ þ denotes the differential ﬂux of the sum over
all three neutrino ﬂavors, i.e. number of neutrinos per unit
energy, area, time and solid angle.
The quasi-differential limit in Fig. 6 takes into accountthe systematic uncertainties. The background rate stays
negligible Oð103 Þ even including the systematic uncertainty and the resultant upper limit is unchanged. The
signal rate uncertainty is strongly dominated by the uncertainty of the NPE yield which inﬂuences the number of
expected signal events as a function of the neutrino energy.
The upper limit is calculated by reducing NPE by 18.5% in
the signal simulation to account for this factor. All theother sources of systematic error only slightly change thesignal passing rate; they are independent of energy. They
are included in the analysis by uniformly scaling theeffective area in the limit calculation.
The present limit is approximately a factor of 20–30
higher than the intensity range expected in the GZK cosmogenic neutrino production models [6,22,23], as one cansee in Fig. 6. The current limit for 242.1 days of observation is comparable to the Auger [32] and HiRes [33]bounds by their multiple year operation.

factor of 20 higher than the predicted GZK neutrino ﬂux
from relatively strongly evolved sources. In the future, datataken by IceCube with 40 to 86 strings operating should
lead to a detection of cosmogenic neutrinos or a greatly
improved limit.
ACKNOWLEDGMENTS

The present work has demonstrated that the IceCube
neutrino observatory is capable of searching for signaturesof EHE cosmogenic neutrinos with relatively straightforward event selection methods. The model independent
differential upper limit obtained with 242.1 days ofobservation in 2007, with approximately one quarterof the completed detector is E2 e þ þ ’ 1:4 
106 GeV cm2 sec1 sr1 for neutrinos with an energyof 3  107 E 3  109 GeV. This is approximately a

We 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 Alumni Research
Foundation, U.S. Department of Energy, and National
Energy Research Scientiﬁc Computing Center, theLouisiana Optical Network Initiative (LONI) grid computing resources; 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 ScientiﬁcResearch (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. Kappes and A. Groß acknowledge
support by the EU Marie Curie OIF Program.
J. P. Rodrigues acknowledges support by the Capes
Foundation, Ministry of Education of Brazil. This analysis
work has been particularly supported by the Japan-US
Bilateral Joint Projects in the Japan Society for the
Promotion of Science.

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ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A
journal homepage: www.elsevier.com/locate/nima

Calibration and characterization of the IceCube photomultiplier tube
R. Abbasi z, Y. Abdou t, T. Abu-Zayyad af, J. Adams o, J.A. Aguilar z, M. Ahlers ae, K. Andeen z, J. Auffenberg al,
X. Bai ad, M. Baker z, S.W. Barwick v, R. Bay g, J.L. Bazo Alba am, K. Beattie h, J.J. Beatty q,r, S. Bechet l,
J.K. Becker j, K.-H. Becker al, M.L. Benabderrahmane am, J. Berdermann am, P. Berghaus z, D. Berley p,
E. Bernardini am, D. Bertrand l, D.Z. Besson x, M. Bissok a, E. Blaufuss p, D.J. Boersma a, C. Bohm ag,
O. Botner aj, L. Bradley ai, J. Braun z, S. Buitink h, M. Carson t, D. Chirkin z, B. Christy p, J. Clem ad, S. Cohen w,
C. Colnard u, D.F. Cowen ai,ah, M.V. D’Agostino g, M. Danninger ag, C. De Clercq m , L. Demirörs w,
O. Depaepe m, F. Descamps t, P. Desiati z, G. de Vries-Uiterweerd t, T. DeYoung ai, J.C. Dı́az-Vélez z,
J. Dreyer s,j, J.P. Dumm z, M.R. Duvoort ak, R. Ehrlich p, J. Eisch z, R.W. Ellsworth p, O. Engdegård aj,
S. Euler a, P.A. Evenson ad, O. Fadiran d, A.R. Fazely f, T. Feusels t, K. Filimonov g, C. Finley ag,
M.M. Foerster ai, B.D. Fox ai, A. Franckowiak i, R. Franke am, T.K. Gaisser ad, J. Gallagher y, R. Ganugapati z,
M. Geisler a, L. Gerhardt h,g, L. Gladstone z, A. Goldschmidt h, J.A. Goodman p, D. Grant ai, T. Griesel ab,
A. Groß o,u, S. Grullon z, R.M. Gunasingha f, M. Gurtner al, C. Ha ai, A. Hallgren aj, F. Halzen z, K. Han o,
K. Hanson z, Y. Hasegawa n, J. Haugen z, K. Helbing al, P. Herquet ac, S. Hickford o, G.C. Hill z,
K.D. Hoffman p, A. Homeier i, K. Hoshina z, D. Hubert m, W. Huelsnitz p, J.-P. Hülß a, P.O. Hulth ag,
K. Hultqvist ag, S. Hussain ad, R.L. Imlay f, M. Inaba n, A. Ishihara n, J. Jacobsen z, G.S. Japaridze d,H. Johansson ag, J.M. Joseph h, K.-H. Kampert al, A. Kappes z,1, T. Karg al, A. Karle z, J.L. Kelley z,
N. Kemming i, P. Kenny x, J. Kiryluk h,g, F. Kislat am, N. Kitamura z, S.R. Klein h,g, S. Knops a, G. Kohnen ac,
H. Kolanoski i, L. Köpke ab, D.J. Koskinen ai, M. Kowalski k, T. Kowarik ab, M. Krasberg z, T. Krings a,
G. Kroll ab, K. Kuehn q, T. Kuwabara ad, M. Labare l, S. Lafebre ai, K. Laihem a, H. Landsman z, R. Lauer am,
A. Laundrie z, R. Lehmann i, D. Lennarz a, J. Lünemann ab, J. Madsen af, P. Majumdar am, R. Maruyama z,
K. Mase n,, H.S. Matis h, M. Matusik al, K. Meagher p, M. Merck z, P. Mészáros ah,ai, T. Meures a,
E. Middell am, N. Milke s, H. Miyamoto n, T. Montaruli z,2, R. Morse z, S.M. Movit ah, R. Nahnhauer am,
J.W. Nam v, U. Naumann al, P. Nießen ad, D.R. Nygren h, S. Odrowski u, A. Olivas p, M. Olivo aj,j, M. Ono n,
S. Panknin i, L. Paul a, C. Pérez de los Heros aj, J. Petrovic l, A. Piegsa ab, D. Pieloth s, A.C. Pohl aj,3,
R. Porrata g, J. Posselt al, P.B. Price g, M. Prikockis ai, G.T. Przybylski h, K. Rawlins c, P. Redl p, E. Resconi u,
W. Rhode s, M. Ribordy w, A. Rizzo m, P. Robl aa, J.P. Rodrigues z, P. Roth p, F. Rothmaier ab, C. Rott q,
C. Roucelle u, D. Rutledge ai, B. Ruzybayev ad, D. Ryckbosch t, H.-G. Sander ab, P. Sandstrom z, S. Sarkar ae,
K. Schatto ab, S. Schlenstedt am, T. Schmidt p, D. Schneider z, A. Schukraft a, A. Schultes al, O. Schulz u,
M. Schunck a, D. Seckel ad, B. Semburg al, S.H. Seo ag, Y. Sestayo u, S. Seunarine o, A. Silvestri v, A. Slipak ai,
G.M. Spiczak af, C. Spiering am, M. Stamatikos q,4, T. Stanev ad, G. Stephens ai, T. Stezelberger h,R.G. Stokstad h, S. Stoyanov ad, E.A. Strahler m, T. Straszheim p, G.W. Sullivan p, Q. Swillens l, I. Taboada e,
A. Tamburro af, O. Tarasova am, A. Tepe e, S. Ter-Antonyan f, C. Terranova w, S. Tilav ad, P.A. Toale ai,
D. Tosi am, D. Turčan p, N. van Eijndhoven m, J. Vandenbroucke g, A. Van Overloop t, J. van Santen i,
B. Voigt am, D. Wahl aa, C. Walck ag, T. Waldenmaier i, M. Wallraff a, M. Walter am, C. Wendt z,,S. Westerhoff z, N. Whitehorn z, K. Wiebe ab, C.H. Wiebusch a, G. Wikström ag, D.R. Williams b,
R. Wischnewski am, H. Wissing p, K. Woschnagg g, C. Xu ad , X.W. Xu f, G. Yodh v, S. Yoshida n,, P. Zarzhitsky b
aIII. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USAc
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USAd
CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USAe
School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USAf
Department of Physics, Southern University, Baton Rouge, LA 70813, USAg
Department of Physics, University of California, Berkeley, CA 94720, USAb0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.nima.2010.03.102

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152hLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, GermanykPhysikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, GermanylUniversité Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, BelgiummVrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgiumn
Department of Physics, Chiba University, Chiba 263-8522, Japano
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealandp
Department of Physics, University of Maryland, College Park, MD 20742, USAq
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH 43210, USAr
Department of Astronomy, Ohio State University, Columbus, OH 43210, USAs
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germanyt
Department of Subatomic and Radiation Physics, University of Gent, B-9000 Gent, BelgiumuMax-Planck-Institut für Kernphysik, D-69177 Heidelberg, Germanyv
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USAw
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerlandx
Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USAyDepartment of Astronomy, University of Wisconsin, Madison, WI 53706, USAz
Department of Physics, University of Wisconsin, Madison, WI 53706, USAaaPhysical Sciences Laboratory, University of Wisconsin, Madison, WI 53706, USAab
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germanyac
Université de Mons, 7000 Mons, Belgiumad
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USAae
Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UKaf
Department of Physics, University of Wisconsin, River Falls, WI 54022, USAag
Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, SwedenahDepartment of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USAai
Department of Physics, Pennsylvania State University, University Park, PA 16802, USAaj
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
ak
Department of Physics and Astronomy, Utrecht University/SRON, NL-3584 CC Utrecht, The NetherlandsalDepartment of Physics, University of Wuppertal, D-42119 Wuppertal, Germanyam
DESY, D-15735 Zeuthen, Germanyijarticle infoa b s t r a c t

Article history:
Received 4 March 2010
Accepted 6 March 2010
Available online 18 March 2010

Over 5000 PMTs are being deployed at the South Pole to compose the IceCube neutrino observatory.
Many are placed deep in the ice to detect Cherenkov light emitted by the products of high-energy
neutrino interactions, and others are frozen into tanks on the surface to detect particles fromatmospheric cosmic ray showers. IceCube is using the 10-in. diameter R7081-02 made by Hamamatsu
Photonics. This paper describes the laboratory characterization and calibration of these PMTs before
deployment. PMTs were illuminated with pulses ranging from single photons to saturation level.
Parameterizations are given for the single photoelectron charge spectrum and the saturation behavior.
Time resolution, late pulses and afterpulses are characterized. Because the PMTs are relatively large, thecathode sensitivity uniformity was measured. The absolute photon detection efﬁciency was calibratedusing Rayleigh-scattered photons from a nitrogen laser. Measured characteristics are discussed in thecontext of their relevance to IceCube event reconstruction and simulation efforts.
& 2010 Elsevier B.V. All rights reserved.

Keywords:
PMT
Neutrino
Cosmic rays
Ice
Cherenkov

1. Introduction
IceCube [1,2] is a kilometer-scale high energy neutrino
telescope currently under construction at the geographic South
Pole. A primary goal is to detect high energy neutrinos fromastrophysical sources, helping to elucidate the mechanisms for
production of high energy cosmic rays [3].

 Corresponding authors. Tel.: + 608 890 0577.

E-mail addresses: mase@hepburn.s.chiba-u.ac.jp (K. Mase),chris.wendt@icecube.wisc.edu, chwendt@icecube.wisc.edu (C. Wendt),syoshida@hepburn.s.chiba-u.ac.jp (S. Yoshida).

1
Afﬁliated with Universität Erlangen-Nürnberg, Physikalisches Institut,
D-91058 Erlangen, Germany.
2
On leave of absence from Universita di Bari and Sezione INFN, Dipartimento
di Fisica, I-70126 Bari, Italy.
3Afﬁliated with School of Pure and Applied Natural Sciences, Kalmar
University, S-39182 Kalmar, Sweden.
4
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA.

IceCube uses the 2800 m thick glacial ice sheet as a Cherenkov
radiator for charged particles, for example those created when cosmic
neutrinos collide with subatomic particles in the ice or nearby rock.
Neutrino interactions can create high energy muons, electrons or tau
particles, which must be distinguished from downgoing backgroundmuons based on the pattern of light emitted. The Cherenkov lightfrom these particles is detected by an embedded array of Digital
Optical Modules (DOMs), each of which incorporates a 10 in. diameter
R7081-02 photomultiplier tube (PMT) made by Hamamatsu Photonics. The DOMs transmit time-stamped digitized PMT signal waveforms to computers at the surface.
The ﬁnished array will consist of 4800 DOMs at depths of1450–2450 m, deployed at 17 m intervals along 80 vertical cables,
which in turn are arranged in a triangular lattice with a horizontal
spacing of approximately 125 m. An additional 320 DOMs will befrozen into 1.8 m diameter ice tanks located at the surface to form
the IceTop array, which is designed for detection of cosmic ray air
2
showers. The geometrical cross-sectional area will be  1 km
3
and the volume of ice encompassed will be  1 km . Another 360
DOMs will be deployed in a more compact geometry (‘‘Deep Core’’[4]) using PMTs almost identical to those described here but witha higher efﬁciency photocathode.

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In this paper we describe measurements characterizing andcalibrating IceCube PMTs, and discuss their relevance to detector
performance and event reconstruction. First we describe thesignals of interest in Section 2. Section 3 brieﬂy describes the
DOMs in which IceCube PMTs are deployed. Section 4 describes
selection and basic features of the PMT, including the darknoise rate. Section 5 presents the design of the HV divider circuit.
Sections 6–9 discuss characteristics of the PMT in the photon
counting regime, starting with single photon waveforms andcharge distributions. Time resolution is studied with a pulsed
laser system. Uniformity of the photon detection response on thephotocathode area is measured by scanning the entire cathodesurface with a UV LED. Absolute efﬁciency calibration of the
IceCube PMTs is carried out using Rayleigh-scattered light from acalibrated laser beam. Sections 10–11 describe response to brightpulses of light, including saturation behavior and afterpulse
characteristics.

2. Characteristics of optical signals in IceCube
We begin by summarizing what the PMTs are supposed todetect, namely the optical signals generated by neutrinos in
IceCube [1,2]. Of particular relevance are the amplitudes andwidths of the pulses, requirements on time resolution, and how
the pulses are used to reconstruct physics events or rejectbackgrounds.
In detection of a high energy nm by IceCube, the neutrino
interaction creates a muon that traverses kilometers of ice andgenerates Cherenkov light along its path. Above 1 TeV, the muon
loses energy stochastically to produce multiple showers of
secondary particles, resulting in an overall light yield proportional
to the muon energy [5,6]. Most light is emitted near the
Cherenkov angle, which is 413 away from the track direction.
The arrival times of detected photons depend on the position ofeach DOM relative to the muon’s path. For close DOMs, mostphotons arrive in a pulse less than 50 ns wide, in which theearliest photons have traveled straight from the muon track
without scattering. Signiﬁcant scattering accumulates along
photon trajectories with a characteristic length scale of about
25 m [7], so light pulses lengthen with distance and reach 1 ms
(FWHM) for DOMs 160 m away from a muon track. Depending on
primary energy and distance from the track, each PMT can see
single photons or pulses ranging up to thousands of photons.
Event reconstruction [1,2,8] builds on principles established
for the predecessor array, AMANDA [9,10]. The observed PMT
waveforms from individual DOMs are correlated and built into
events, which are ﬁtted to physics hypotheses using the
maximum likelihood method. Each ﬁt has access to the complete
pattern of light amplitude and timing seen by the DOMs, andaccounts for the DOMs’ time response and optical sensitivity as
well as time dispersion and optical attenuation introduced by theice. The ﬁt gives the direction and energy of the muon, which inturn characterizes its parent neutrino.
The observed light pattern is also used to distinguish the rare
neutrino events from the large background of muons created incosmic ray air showers, which are 106 times more numerous. For
this the reconstructed direction is key, because neutrinos cancome from any direction, even up from below, but the backgroundmuons are downgoing. A small fraction of background events canbe misreconstructed in direction, thereby appearing to come fromneutrinos, but the pattern of detected light will generally be apoor match compared to expectations for a properly reconstructed track. Misreconstruction can be aggravated by additionalmuons from the same shower or other coincident showers. This
separation between signal and background is accomplished by

60

141

evaluating relative probabilities on an event-by-event basis, andis aided by good time and amplitude resolution as well as by low
PMT noise rates.
Similar principles apply to other types of high energy neutrino
interaction. Instead of a muon, an electron can be created thatloses its energy in a few-meter-long particle shower [11]; on thescale of IceCube, such a shower appears almost like a point sourceof Cherenkov light. For a sufﬁciently energetic neutrino, the light
can be detected hundreds of meters away, and nearby DOMs cansee enough light to drive their PMTs into the nonlinear saturation
regime. Therefore proper modeling of saturation behavior isneeded for good reconstruction and background rejection.
Design studies [2] for important physics goals have shown that
sufﬁcient reconstruction quality is achieved for a PMT timing
resolution of 5 ns, low-temperature noise rate below 500 Hz, andeffective dynamic range of 200 photoelectrons per 15 ns.
In the case of lower energy (MeV) neutrinos from supernovae,
IceCube cannot resolve individual interactions. Instead, supernovae
would be detected as a momentary increase in the collective photon
counting rate for the whole array, corresponding to a large numberof neutrino interactions within a few seconds. The dark noise rate of
the PMTs is particularly important here, because it dictates thestatistical signiﬁcance of any excess count rate.
IceTop uses DOMs identical to those in the deep ice. Here thesignals arise from muons, electrons and gamma rays in cosmic ray
air showers [12]. These particles deposit energy in the ice tanks
housing the DOMs, resulting in light pulses up to several hundred
nanoseconds long. The arrival times and amplitudes in the surface
array are then used to reconstruct the shower core position,
direction, and energy. An overall timing resolution of 10 ns
provides pointing accuracy of about 11. The PMT pulses range
from single photoelectrons at the periphery of showers to 105
photoelectrons for a 1 EeV shower that strikes within the array. To
achieve the implied dynamic range, each tank contains two DOMs
operating at gains differing by a factor 50.

3. The IceCube optical detector: DOM
The Digital Optical Module is the fundamental element for
both optical detection and data acquisition in IceCube [2,13,14]. It
contains a 10 in. diameter PMT supported by coupling gel, thePMT high voltage generator and divider circuits, an LED ﬂasher
board used for calibration of the array geometry and study of ice
properties, and the DOM mainboard which contains the analog
and digital signal processing electronics [14]. The PMT issurrounded by a mmetal grid to shield it from the terrestrial
magnetic ﬁeld and improve the PMT performance. All systems arehoused within a pressure sphere made of 0.5 in. thick glass,capable of withstanding pressures to 70 MPa. The glass and gel set
the short wavelength cutoff of the DOM at about 350 nm, where
the PMT by itself is still relatively efﬁcient.
Strings of DOMs are deployed into water columns that havebeen melted by a hot-water drill. After refreezing, DOMs are
optically well coupled to the surrounding glacial ice. Signal andpower connections between the DOMs and the surface areprovided by copper twisted-pair wires bundled together to form
the main cables. PMT signals are digitized on the mainboard,
buffered in memory, and sent to the surface upon command of
surface readout processors.

4. PMT selection and dark noise rate
A number of large-area PMTs are commercially available andhave been used successfully to instrument large volumes in otherARTICLE IN PRESS
R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

experiments. IceCube selected the R7081-02 made by Hamamatsu
Photonics, emphasizing the criteria of low dark noise and goodtime and charge resolution for single photons. Some manufacturer’s speciﬁcations are shown in Table 1, and more detailed
measurements are described in the following.
The nominal gain of 107 was chosen to give single photon
pulses around 8 mV, which is well above the digitizer precisionand other electronic noise levels (both  0:1 mV). Aging was not aconcern for gain selection, since at the expected noise rates, thecorresponding total charge delivered by each deep-ice PMT willbe less than 1 C after 20 years (or 100 C for IceTop). Tubes with 10
and 12 stages were evaluated, with the 10 stage options showing
a better peak-to-valley ratio at this gain. Lower gains of 5  106
and 105 were chosen for IceTop PMTs because air shower pulses
generally comprise many photon detections.
The R7081-02 has 10 linear focused dynode stages andachieved the nominal gain of 107 at about 1300 V in our tests
with the recommended divider ratios (observed range 1050–
1600 V for 3744 PMTs). Its 10 in. diameter photocathode iscomposed of the standard bialkali material (Sb–Rb–Cs, Sb–K–Cs)
with a peak quantum efﬁciency of approximately 25% at 390 nm.
With a borosilicate glass envelope, the spectral response [16] is agood match to the spectrum of Cherenkov light after propagation
through ice [7], especially considering the 350 nm cutoff of the
housing.
In response to IceCube requirements, the supplied R7081-02
units were manufactured with a custom low radioactivity glass.
The resulting dark count rate at low temperatures is close to
300 Hz in the 40 to 20 3 C range of greatest interest for IceCube(Fig. 1). The higher room temperature rate can be attributed
mostly to cathode thermionic emission, which is suppressed at
low temperature. The low temperature rate is believed to be
dominated by radioactive decays plus scintillation in the PMT
glass envelope, and shows a rise with decreasing temperaturesimilar to that reported in other studies [17]. The association ofthis rate with decays is supported by time correlations observedon scales up to 1 ms, as can result from delayed particle capture orde-excitation of states created by decays. It is also supported by
the observed effect of taping: for these measurements, the entire
outside surface of the PMT glass was covered in black vinyl tape,pulled tightly against the glass to avoid bubbles. The taping isobserved to reduce the low-temperature noise rate by about half.
The reduction is attributed to absorption of outward going decay
photons, which can otherwise be channeled to the photocathodevia internal reﬂection. The taped result is appropriate for PMTs
installed in IceCube DOMs because they are optically coupled togel (then glass and ice) where the refractive index matches better
than it does for air.
The low dark rate allows IceCube to record all events thatsatisfy simple multiplicity conditions, and is particularly important for observation of any galactic supernova event. Such asupernova could yield about 106 excess photon counts in IceCube
over a few seconds [18]. The single-PMT dark rate, multiplied by
the number of PMTs, contributes a background rate of
1:5  106 Hz, with a similar contribution from decays in the

Table 1
Hamamatsu speciﬁcations for the R7081-02 PMT (typical) [15].
Spectral response
Quantum efﬁciency at 390 nm
Supply voltage for gain 107
Dark rate at 40 3 C
Transit time spread
Peak to valley ratio for single photons
Pulse linearity at 2% deviation

300–650 nm
25%1500 V
500 Hz3.2 ns
2.5
70 mA

Dark count rate (Hz)

142

1000

500

0
–80

–60

–40
–20
Temperature (°C)

020

Fig. 1. Dark count rate versus temperature for a sample IceCube PMT covered withblack tape (see text). Rates were recorded after a settling time of 12 h of dark
operation at gain 107 and discriminator threshold 0.25 times the single
photoelectron peak. An artiﬁcial deadtime circuit rejected additional hits within
6 ms of each count, including about half of all afterpulses (Section 11). The
contribution from cosmic rays (o 5 Hz) has not been subtracted.

DOMs’ glass housing. The excess from a supernova would be
easily observed above this background, even including the detailsof its time structure.
On the other hand, a high energy neutrino event creates opticalpulses distributed over 3 ms, with most information contained
within a time window less than 300 ns wide in each DOM.
Because this window is so short, the low PMT dark rate implies
that only 1% of muons would be accompanied by a relevant noise
count among the 100 DOMs closest to the track, and many ofthese DOMs detect multiple signal photons. Therefore thedegradation of reconstruction and background rejection is verysmall. The dark noise rate has even less effect for IceTop DOMs,
due to higher thresholds and coincidence requirements.

5. High voltage divider circuit
The relative dynode voltage ratios for R7081-02 have been
optimized by Hamamatsu to achieve a maximum collection
efﬁciency while achieving 107 gain between 1050 and 1600 V.
Our high voltage subsystem design fulﬁlls the additional requirements of low power consumption, long-term reliability, andsustained response to very bright pulses lasting up to a
microsecond.
The dynode voltages are provided by a passive resistive divider
with a total resistance of 130 MO (Fig. 2). The rather high total
resistance is chosen to minimize power consumption, which is an
important economic consideration for operations at the South
Pole. A custom, compact, high voltage generator [19] that is both
low power ( o 300 mW) and low noise ( o 1 mV ripple, peak-topeak) is used in conjunction with the passive divider.
Capacitors are placed across the last six dynode intervals andbetween the last dynode and anode. These capacitors help sustain
the PMT output for large pulses of up to 106 photoelectrons (p.e.).
Even for illumination in the PMT saturation region (  200 p:e:=ns,
see Section 10), the transient gain loss after a 1 ms pulse(2  105 p.e.) is observed to be less than 1%. A detailed simulation[20] indicates that such a pulse could arise from a 50 PeV electron
shower 100 m away from the PMT, which would then be faithfullyrecorded. Pulses up to ﬁve times this large (106 p.e.) still result inless than 20% transient gain loss, so while the primary pulse
would be completely saturated, afterpulse amplitude could be
used to estimate the total illumination (Section 11). Finally above

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

K

DY1 F2F1 F3DY2

DY3 DY4DY5 DY6DY7 DY8

DY9 DY10

R13
100

R15
100

R14
100

143

P

Front-end
Amplifier
T1

95Ω

R16
100

95
+

R1
52.5M

R2
R3
R4
R5
R6
R7
R8
R9 R10 R11
1.9M 10.5M 15.4M 10.2M 5.1M 3.1M 3.7M 4.6M 6.8M 9.3M

R12
7.5M

Pedestal

–

R17
100K
Ferrite

C1
C2
C3
C4
C5
C6
C7
3.3nF 4.7nF 4.7nF 4.7nF 10nF 10nF 22nF

R18
100K

+

–

PMT High Voltage
Fig. 2. Schematic of the passive HV divider circuit, shown with coupling to the front-end ampliﬁer on the digitizer board.

62

0
Signal (mV)

2  107 p.e. the gain loss rises rapidly above 50%. For all thesetransient gain losses, recovery occurs within the RC time
constants of order 1 s.
Low-inductance resistors (100 O, R13 through R15) are used todampen ringing that arises from coupling of the larger dynodeﬁlter capacitors with parasitic inductance in the dynode leads andprinted circuit traces. This ringing could otherwise be a nuisancewhen reconstructing a single PMT output waveform as a series ofphoton hits.
The IceCube PMTs are operated with their cathode at ground
potential. Therefore the high voltage anode is AC coupled to the frontend ampliﬁers. For the AC coupling, we use a custom biﬁlar-wound
1:1 toroidal transformer rather than a DC blocking capacitor. High
voltage reliability is achieved in the transformer winding using wirewith insulation rated for over 5 kV DC. The resulting stray capacitancefrom anode to front-end ampliﬁer is only 30 pF, which limits thestored energy which might damage the analog front-end if sparking
should occur in the HV system. In contrast, a coupling capacitor large
enough to meet the signal droop speciﬁcation would be at least 1000
times larger than the stray capacitance of the transformer. The
transformer topology also reduces noise by avoiding noisy highvoltage ceramic signal coupling capacitors and by breaking a groundloop path involving the HV power supply. The ferrite and resistors inseries with the HV supply further reduce coupling of high frequency
noise to the front end input.
The transformer coupling delivers good signal ﬁdelity for singlephotoelectron (SPE) waveforms with risetimes of a few ns, whiletransmitting wide pulses exceeding 1 ms with less than 10% droop
and undershoot. The custom design uses 18 biﬁlar turns on a ferrite(Magnetics Type H) toroid core, providing roughly ﬂat coupling from
8 kHz to over 100 MHz at operating temperatures down to 40 3 C.
The self-resonant frequency is above 150 MHz. The low operation
temperature presented a challenge because the permeability of thetransformer core decreases rapidly with temperature, leading to ashorter droop time constant. Although most DOMs have a time
constant around 15 ms at ambient temperatures near 30 3 C, 1200
DOMs were built using an older transformer design yielding a time
constant around 1:5 ms at 30 3 C. The improved performance of the
new design was achieved with a larger core and more turns, at theexpense of a slightly wider SPE pulse shape (Fig. 3). The two designs
are deployed intermixed.
The droop and undershoot are relevant for the ms long trains ofphoton pulses expected in DOMs over 100 m away from high

–4

–8
0

20
Time (ns)40

Fig. 3. Average of 10,000 SPE waveforms for one PMT at gain 1  107, as seen at
the secondary of the AC coupling transformer. Results for other PMT samples arevery similar. The solid and dashed curves correspond to new and old transformer
designs discussed in Section 5.

energy events, such as 10 TeV electron showers or 500 TeV muontracks. The small remaining effects are corrected by a software
digital ﬁlter as a ﬁrst step in event reconstruction, based on
individual time constants for each DOM. The residual error istypically less than 1% of the pulse amplitude (except for pulses
with peak or undershoot outside the ADC dynamic range, which islimited after 400 ns [14]).
The divider circuit is constructed on a 10 cm-diameter printed
circuit board which is directly solder-mounted to the PMT. Allcomponents (except R13–R16) are through-hole mount type,selected with a voltage derating factor of two or greater (typicallyfour) to ensure long-term reliability. Strict voltage and voltage
gradient rules are applied to the board layout.
Coaxial cables are used for the connections to the high voltage
generator and the front end ampliﬁer on the digitizer board. The
effective load for anode output pulses is 50O (43O for the oldertransformer design), which includes a back-termination resistor
on the primary side of the transformer (R16), the transformer AC
response, and the input impedance of the ampliﬁer.

6. Single photoelectron waveform and charge
The SPE waveform shape and charge probability distribution
are important for event reconstruction. The DOM waveform

ARTICLE IN PRESS
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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

coincidences of noise pulses such as from thermionic emission at
the dynodes. The check for a noise contribution was done with the
LED light output disabled (but not the synchronization signal thattriggers acquisitions); all counts outside the narrow pedestal
region were greatly suppressed compared to Fig. 4.
The low-charge component has been described in the past for
many PMTs [21], and has been attributed to a sizable probability
for backscattering of the primary photoelectron at the ﬁrst
dynode [22,23], leading to events where only a few secondaries
are produced instead of the usual 10–20.
The shape of the low-charge component is important becauseeven small pulses below the DOM’s trigger threshold will berecorded in events with multiple photoelectrons. Therefore event
reconstruction should account for the entire charge probability
distribution down to zero charge, which we model as a Gaussianplus an exponential term [21]:
"
#


Pe
q
1
ðqq0 Þ2
þ ð1Pe Þ pﬃﬃﬃﬃﬃﬃ
:
ð1Þ
exp 
exp 
f ðqÞ ¼
qt
qt
2s2q
2psq
Here Pe is the fraction of events in the low-charge exponential
part, q0 is the charge at the SPE peak which deﬁnes the PMT gain,
sq is the width of the Gaussian ﬁt around the SPE peak, and qt isthe decay constant in the exponential component. Fig. 4 showsthat this is a good model for the shape of the charge histogram
away from the pedestal.
Fig. 5 shows results of ﬁtting equation (1) for a large sample of
PMTs at different gains above 5  107, excluding the very low
charge region q o 0:15q0 and the very high charge region morethan 2s past the peak. The value of qt =q0 is substantiallydegenerate with Pe for describing observed spectra in the ﬁtted
range, so it has been ﬁxed at the representative value of 0.20. The
scaled quantities sq =q0 , qt =q0 , and Pe are found not to varystrongly with the PMT gain. The very small pulses with q o0:15q0
were omitted to avoid confusion with the tail of the pedestal
distribution; results were the same if the low-charge cut was
moved to 0.25q0. The charge resolution sq =q0 has been separately
studied for gains between 107 and 108 and again no signiﬁcantvariations were seen.
Fig. 5 also shows the spread in parameters from PMT to PMT.
The distribution in each parameter is approximately Gaussian,

0.4
Pe

digitizers are triggered when the signal reaches about 0.25 times
the typical SPE peak amplitude, after which the PMT output
waveform is digitized for up to 6:4 ms. The detection efﬁciency forsingle photons depends directly on the fraction of the SPE charge
distribution above trigger threshold. For high energy neutrino
events, many waveforms show contributions from multiple
photons, all of which could provide useful information during
event reconstruction. The overall light yield provides an estimateof the neutrino energy, and the space and time distribution oflight helps to reconstruct direction and reject backgrounds. The
time distribution of photons can be extracted from each PMT
waveform if the response to single photons is well understood.
The response to each photon is approximately given by theaverage SPE waveform, scaled randomly according to thecomplete charge probability distribution.
In order to mimic the ambient temperature in the ice, PMTs
were placed in a freezer box at 32 3 C and illuminated by diffusedlight from a 375 nm UV LED. The light was generated in 10 ns
pulses with intensity of about 0.1 photons per shot (  0:02
photoelectrons per shot), dim enough to initiate only SPE signals.
Fig. 3 shows the average SPE waveform, measured at theoutput of the AC coupling transformer with a digital storage
oscilloscope (LeCroy LT374, 500 MHz bandwidth, 0.5 ns samples).
Here the 95 O input impedance of the DOM’s front end ampliﬁer
was replaced by the series combination of a 50 O resistor and theoscilloscope input.
Individual waveforms have different amplitudes but theirshapes are similar to within a few percent. The waveform isdominated by a peak of Gaussian shape (s ¼ 3:2 ns) which
accounts for 83% of the area. A tail on the late side of the peakaccounts for the remaining area and exhibits a small amount ofringing. About 90% of the charge is collected before 10 ns after the
peak. A substantial part of the observed pulse width is attributed
to the damping resistors and the coupling transformer (Section 5).
To study the total charge in SPE events, a computer-controlled
integrating ADC module (LeCroy 2249A) was used to integrate
charge in a 70 ns window, triggered by the synchronization signalof the LED pulse generator. Fig. 4 shows a typical charge
histogram, which exhibits a clear SPE peak to the right of thepedestal peak. The Gaussian part of the SPE peak corresponds to acharge resolution of approximately 30%.
The non-Gaussian component rising below 0.3 times the SPE
charge in Fig. 4 has been studied to verify that such small pulses
actually reﬂect in-time detection of photons, and not accidental

Data

106

0.2

Model
Model (Scaled)
0Gaussian Fit

104

0

5

0

5

10

15

10

15

Pedestal Fit
103
0.4

102
σq / q0

Counts per bin

105

101

0.2

0

10

0

5

10
Charge (pC)

15

20
0
7

Fig. 4. Typical pedestal-subtracted SPE charge histogram at gain 5  10 ,including pedestal peak. Fits refer to Eq. (1), with the constraint qt =q0 ¼ 0:2. The
remaining parameters are optimized to ﬁt this histogram for the curve labeled‘‘Model’’, while ‘‘Model (Scaled)’’ optimizes only the scale parameter q0 while
holding sq =q0 and Pe at values that describe the average of 120 PMTs.

Gain / 107
Fig. 5. Scaled parameters from Eq. (1) as a function of PMT gain. The error bars
show the 1s spread in parameters obtained for a sampling of 115 PMTs.

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

with the width shown by the error bars. The spread is substantial,
but is not expected to have a large effect on data analysis, so the
IceCube PMTs do not need to be parameterized individually.
Instead, an average model is currently used in event simulation
and reconstruction, without modeling the spread. The similarity
among PMTs can also be gauged from Fig. 4, where data from one
PMT is compared with a model curve scaled from the average ﬁtresults for 120 PMTs.
The above measurements were performed with diffuse lightand represent an average over the photocathode surface. In a
separate measurement at gain 107, substantial differences wereobserved as a function of position; for example, the peak-to-valley
ratio decreased to near unity close to the edge of the photocathode, compounding the effects of gain variation (Section 8).

7. Time resolution
The timing of recorded SPE waveforms, relative to the photon
arrival time, was studied at 40 3 C using fast pulses (FWHM 50 ps)
from a Hamamatsu PLP-10 diode laser. Pulses were opticallyattenuated and diffused over the PMT face, yielding an average of0.04 photoelectrons per shot. The wavelength was 405 nm.
Each PMT was set for gain 107 based on its SPE charge
spectrum. Hits greater than 0.4 times the SPE charge wererecorded using the DOM digitization and readout electronics.
Synchronization pulses from the laser were also digitized toindicate the true photon arrival times to within a ﬁxed offset. Hittimes were deﬁned as the points where each waveform reached
50% of its maximum, resulting in the time resolution histogram ofFig. 6.
The main peak of the time histogram has width equivalent to a
Gaussian of s ¼ 2:0 ns, although the rising and falling edges of thepeak ﬁt better to half-Gaussians with s ¼ 1:2 and 2.7 ns,
respectively. Some of the width can be attributed to simultaneous
illumination of the entire photocathode in our tests. Whenilluminated at the center only, the width decreased to 1.5 ns;
conversely, the outer 3 cm of the photocathode exhibited
additional delay of about 3 ns and additional broadening. The
data acquisition system contributed a time smearing of less than
0.6 ns, which has not been subtracted.

105

Counts / ns

104
103
102
101
100
–50

0

50

100

150

Hit time (ns)Fig. 6. Typical distribution of SPE hit times for an IceCube PMT, when illuminatedby narrow pulses from a diode laser. Counts are shown for 1 ns time bins,
referenced to a laser synchronization pulse. A small fraction of late pulses (dashedline) are due to laser afterglow plus the random background count rate; hit
fractions described in the text are corrected accordingly. The random backgroundalso explains the counts before the synchronization pulse.

64

145

About 4% of hits are found in a shoulder (25–65 ns) andsecondary peak at 71 ns, and 0.2% make up a corresponding
tertiary structure (85–160 ns). The delayed hits are believed toarise when an electron trajectory is scattered back from the ﬁrst
dynode towards the photocathode, where it turns around andthen eventually arrives back at the ﬁrst dynode to initiate thepulse [23–25].
Because of strong photon scattering in the ice, the dispersion of
hit times by the PMT at the 2 ns scale is not a limiting factor forreconstruction in IceCube; likewise for the tail at late times.
Considering the spacing between DOMs, photons must typicallytravel tens of meters before detection, which is comparable to thescattering length of around 25 m [7]. A detailed simulation ofphoton scattering [26] showed that at 10 m distance, about 40% of
photons are delayed by more than 5 ns, and 10% of photons aredelayed between 20 and 80 ns. This is larger than the corresponding effects from the PMT itself. On the other hand, DOMs close to ahigh energy track can be expected to detect at least one photonwith negligible delay, and then the very small 1.2 ns dispersion on
the early side of the time resolution peak may be relevant whenreconstructing arrival time of the earliest photon or the pulse risetime.
The time resolution study also reveals DOM-to-DOM differences in the nominal delay of SPE waveforms relative to photon
arrival time. This delay includes PMT transit time plus signal
delays between the PMT output and the digitizer. The PMT transit
time is found to vary according to the square root of the applied
voltage,pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð2Þ
Ttransit ðVPMT Þ ¼ T0 þ 2kV0 V0 =VPMT
where k ¼ 0:017 ns=V is the slope at V0 ¼1500 V. The voltage
applied to each PMT is set for a design gain 107, which is achieved
between 1050 and 1600 V in 99.9% of PMTs. The resulting RMS
spread of the overall time offset is 2.7 ns. We ﬁnd 5% of DOMs
more than 5 ns away from the mean, so the DOM-to-DOM
corrections are currently included in reconstruction.

8. Two-dimensional photocathode scan
The number of photons arriving at the PMT is calculated fromthe observed photoelectron signals via the PMT optical efﬁciency.
This is separated into an overall ‘‘absolute efﬁciency’’ and anangular dependence. The dominant factor in angular dependence
is just the amount of photocathode area which can be seen fromvarious directions. However, this has to be adjusted for the factthat the photocathode surface is very large and different portions
do not all yield the same efﬁciency.
We have systematically analyzed the variation of efﬁciency
with photocathode position at 25 3 C, using a two-dimensional
scan system. A UV LED (370 nm) with collimator produced a 1 mm
spot which was moved along the curved PMT surface, maintaining
normal incidence of the light. The LED delivered approximately
125 photons per 80 ns pulse. The anode voltage was set for gain
107 at the center of the photocathode, as measured by the SPE
charge peak (q0 in Eq. (1)). The PMT pulse charge for each position
was then measured by an integrating ADC triggered by the LED
pulser.
Fig. 7 shows typical response maps on the cathode surface. The
measured charge is proportional to the net photomultiplierefﬁciency and reﬂects the combined position dependence ofphotocathode quantum efﬁciency, collection efﬁciency, anddynode multiplication. PMT to PMT variation of the efﬁciency at
a given spot on the photocathode may be as great as 40%,
however, the spread in the area-integrated efﬁciency from PMT to
PMT is much smaller, of order 10% (see Section 9). The average

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Fig. 7. Position dependence of the light pulse response for three example PMTs, and the average of 135 PMTs (lower right). The X–Y coordinates measure distance from thecenter of the photocathode along the curved PMT face. The value at each X–Y position indicates the PMT output pulse charge in units of the SPE charge, averaged over many
pulses.

map shows a uniform falloff in the edge region, except for a small
bias in the + X direction. All PMTs were measured in the sameorientation, so this bias could be associated to the ﬁrst dynode
position or the geomagnetic ﬁeld.
A small part of the variation seen in the scans can be attributed
to systematic errors, which arise mainly from the geomagnetic
ﬁeld and LED luminosity variance. The geomagnetic ﬁeld of
462 mG is attenuated by about 50% with a shield made of m- metal
sheet and wire, as also used in IceCube DOMs. By comparing
measurements with the PMT rotated from its standard orientationin various ways, we determined the ﬁeld’s effect on the efﬁciency
variation is about 10%. Because the magnetic shield is the same,the overall results are representative of what is expected for
deployed IceCube DOMs. (The ﬁeld at the South Pole is 553 mG,and more vertical relative to the PMT axis.) The time dependenceof LED luminosity affected the shape of each scan by less than 2%,
as seen by reproducibility of the scan results.
By reducing the light intensity to give only SPE hits, a similar
map has been constructed for gain variation. The gain can vary as
a function of position because the corresponding photoelectron
trajectories arrive differently at the ﬁrst dynode, leading todifferent yields of secondary electrons. The observed gain (deﬁned
by q0 in Eq. (1)) varies within 7 10% over the active region whenhigh voltage is set for gain 5  107 at the center. However, thelow-charge contribution to the SPE charge spectrum (Pe in Eq. (1))
was found to also vary with position, so that the peak-to-valley
ratio decreases close to unity near the edge of the photocathode.
In this way, the average charge delivered per photoelectron wasobserved to decrease by up to 30% at nominal gain 107. Because of
these effects, the detection efﬁciency map for single photons
using a speciﬁc discriminator threshold can differ somewhat fromthe maps of Fig. 7.
The integrated sensitivity for a broad beam of photons incident
from a particular direction follows from the cathode efﬁciency
maps by averaging over the surface seen from that direction [27],with correction for non-normal incidence on surface elements asappropriate [28]. For this purpose the relative efﬁciency map isassumed not to vary with wavelength, i.e., each position isassumed to obey the spectral response curve given by the
manufacturer [16]. The averaging substantially reduces the effectof variations over the surface so the sensitivity is not strongly
dependent on direction at moderate polar angles. Only light that
arrives at large polar angles relative to the PMT axis will primarily
illuminate the equator region and therefore show strong azimuthal dependence. Likewise, the variation in charge spectrum
from center to edge has little effect after averaging.
The scans were performed on a small fraction of the IceCube
PMTs, so only the average variation with polar angle is used in

65

ARTICLE IN PRESS

9.1. Technique
Our setup for measuring a PMT’s UV photon detection efﬁciency isshown in Fig. 8. A pulsed 337 nm laser beam is passed through achamber containing pure nitrogen gas, and the PMT to be calibrated isilluminated by the tiny amount of light that is Rayleigh scattered atabout 901 from the beam. The PMT is rotated inside the dark box toprobe different positions on the photocathode surface. The primarybeam intensity is measured with a calibrated silicon photodiode‘‘energy probe’’, and sets the fundamental scale for our efﬁciency
measurement. A pressure gauge and temperature sensor provide thegas density. Beam intensity, geometry and gas density are then foldedwith the well-known Rayleigh scattering cross-section to obtain theabsolute number of photons per pulse incident on the PMT. Individual
photon detections are counted in each pulse and divided by the
number incident to obtain the optical sensitivity at 337 nm.
Additional corrections (Section 9.4) are needed to obtain DOM
efﬁciency at wavelengths around 400 nm where IceCube is mostsensitive.
The measurement combines effects of quantum efﬁciency andcollection efﬁciency, and can be directly applied in IceCube
analysis. It is different from the usual quantum efﬁciency
measurement, which is based on cathode current response to acalibrated DC light source [16,30].
The laser (Spectra-Physics VSL-337ND-S) emits 4 ns pulses
containing  1010 photons, as measured by the silicon photodiode probe (Laser Probe, Inc., RjP-465). After a warm-up delay,
pulse energies are stable to within 72%.
The beam width is 1 mm, so the illuminated gas volume may beconsidered as a line source of Rayleigh scattered light. Apertures
between the beam and the PMT deﬁne a source region with effective
length of about 1 cm and a spot size on the PMT of about 1.5 cm.
Photons can reach the PMT if they are scattered from the source
region into a solid angle of about 7.6  10  4 sr around the 903

66

147

Photodiode 2

Iris (1mm)
Shutter
Neutral Density Filter (1%)
Neutral Density Filter (0.1%)
Polarizer (45°)
Depolarizer
Chamber, 60cm DIA

9. Absolute efﬁciency calibration
The absolute calibration of PMT optical efﬁciency is importantbecause IceCube uses the observed number of photons to estimate
energy in reconstructed neutrino interactions. Showers initiatedby electrons or tau leptons yield light in proportion to the energy,
and so do muons above 1 TeV where energy loss is dominated bydirect pair production, photonuclear interactions and bremsstrahlung [5,6].
Optical efﬁciency can be studied after deployment by using
light from muons (produced in cosmic ray showers above
IceCube) or from calibrated beacons deployed in the ice nearby.
However, it is hard to isolate the PMT response from the effects oflight scattering and attenuation in the ice, which have someuncertainties [7].
Here we describe the laboratory calibration of standard PMTs
installed in 16 IceCube DOMs distributed throughout the array.
The calibrated PMTs provide direct information for the energy
calibration of IceCube, and will also help clarify the ice effects inother studies, which is an important subject on its own.

337 nmsimulation and reconstruction. For IceCube, the remaining PMTto-PMT variation in directional sensitivity has very small
consequences, because light is typically scattered after travelingabout 25 m through the ice, and additional scattering takes placein the refrozen ice in the hole where the DOMs are deployed. The
PMT-to-PMT variation, as well as the position dependence itself,
could be more important for detectors deployed in water where
scattering lengths are much longer [29].

Laser

R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Backward
PMT (H7195)

R7081-02 PMT

Forward
PMT (H7195)

Rotation Stage

Photodiode 1
Fig. 8. Schematic view of the absolute calibration system. Photodiode 1
establishes the beam intensity, which is used to predict the amount of Rayleighscattered light reaching the R7081-02 PMT. The Hamamatsu H7195 PMTs and theother photodiode are for monitoring. Optical bafﬂes deﬁne the scatteringgeometry, and chamber windows are anti-reﬂection coated UV quartz (R o 0:1%
at 337 nm).

direction, while other scattered photons are eventually absorbed on
bafﬂes or other surfaces inside the chamber.
The Rayleigh scattering cross-section for a circularly polarized
beam on nitrogen gas is taken as [31]dsR
3¼
ð1þ cos2 yÞ  ð3:50 7 0:02Þ  1026 cm2
dO
16p

ð3Þ

with y as the polar angle relative to the beam direction. The
geometrical integration over the source region and corresponding
solid angles is handled in a detailed ray-tracing calculation. Afteraccounting for pressure and temperature, this yields the overall
number of scattered photons reaching the PMT, typically 0.5 perpulse. With detection efﬁciency around 20%, this corresponds to 0:1 SPE per pulse.
For counting photon detections, the PMT output charge is
integrated for each laser pulse with a CAMAC ADC. The gatingtime is 184 ns which is long enough to include the late PMT pulses
described in Section 7. The PMT gain is set close to 108 as deﬁned
by the SPE peak, q0 in Eq. (1). We then count the number of eventswith charge q greater than a threshold qth ¼0.5q0, which can beclearly discriminated in the charge histogram. A small correction
for events with multiple photoelectrons yields the number ofdetected photons with q 4qth .
The PMT efﬁciency Z for qth ¼0.5q0 is then given by comparing
the number of detected photons to the number reaching the PMT.
The efﬁciency for other charge thresholds can be computed byextrapolation with the SPE charge response model, Eq. (1).
9.2. Results
Fig. 9 shows the measured detection efﬁciency as a function of
distance from the cathode center. It also shows that the absolute

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Fig. 9. Detection efﬁciency as a function of distance from the cathode center for three different PMTs. The points with error bars show absolute efﬁciency measurements
extrapolated to qth ¼ 0. The histogram curves show corresponding results from the 2D relative efﬁciency scans (Section 8) after normalization. Systematic uncertainties forthe histograms are described in Section 8.

Table 2
Measured photon detection efﬁciency (Z) and photon effective area (Aeff) at 25 3 C
for four different PMTs at wavelength 337 nm and gain 108.
PMT

Zcenter (%)(qth ¼0.5q0)
TA1895
TA2086
TA2349TA2374

16.4
16.5
15.1
16.4

Zwhole (%)(qth ¼0.5q0)

13.2
13.6
12.1
13.0

Zwhole (%)(qth ¼ 0)

Aeff (cm2)(qth ¼ 0.5q0)

Aeff (cm2)(qth ¼ 0)

18.6
18.8
17.6
17.8

84
87
77
83

119
120
112
114

Values for qth ¼ 0 were extrapolated using Eq. (1), where model parameters wereﬁt independently for each PMT.

efﬁciency measurements follow closely the shape expected fromthe 2D relative efﬁciency scans (Section 8). Consequently, therelative efﬁciency scans can be normalized to the absolutemeasurements and used to estimate the absolute efﬁciency
averaged over any given area of the photocathode surface.
Table 2 lists measured efﬁciencies at the center and averaged
over the whole photocathode area. The latter is deﬁned to include
all points within 15 cm of the PMT axis, measured along the
curved surface. Table 2 also includes the photon ‘‘effective area’’
which means the amount of ideal surface with 100% efﬁciency
that corresponds to the actual convolution of area and efﬁciency.
Here it is quoted for light uniformly spread over the PMT surface,with normal incidence. For use in IceCube analysis, a similarcalculation is performed for unidirectional beams as a function of
the beam angle, folding in the variation of cathode response andoptical effects at material boundaries.
The detection efﬁciencies in the central area of the photocathode are close to 20% if extrapolated to qth ¼ 0. These values
have been compared on a PMT-by-PMT basis with measurements
by Hamamatsu using cathode response to DC light sources. We
ﬁnd very good agreement, which implies that the collection
efﬁciency is not much less than 100% at the cathode center.
IceCube PMTs operate at lower voltages than used in thismeasurement (gain 107 instead of 108), so collection efﬁciency is
expected to be slightly lower. However, this effect is expected tobe concentrated at the edges where the electron optics are lessideal, and the efﬁciency falloff near the edges is obtained from the2D relative efﬁciency scans (Section 8). Since those scans weredone at gain 107, no additional correction is necessary for the
results in Table 2.
9.3. Uncertainties
The overall systematic uncertainty DZ=Z of the PMT detection
efﬁciency measurement is 7.7%, as detailed in Table 3. In addition,
the measurement of each position on the PMT face has a typicalstatistical uncertainty of about 5%, set by the number of SPE hits
recorded. This is reduced to about 2% when calculating efﬁciency

Table 3
Systematic error budget for the PMT efﬁciency calibration.
Source

DZ=Z (%)

Laser beam energy
Aperture
Ambient magnetic ﬁeld
Pressure and temperature
Polarization
Rayleigh cross-section
Dark noise/cosmic rays

5
4
4
1
1
0.5
0.2

Overall

7.7

for the whole PMT by combining information from the individual
face positions, but the extrapolation relies on the 2D map (Section8) which has comparable uncertainties.
The dominant contributions to systematic error arise from thelaser beam energy measurement, the geometry of the scatteringchamber, and the geomagnetic ﬁeld. The ﬁrst two enter directly
into the calculation of the number of photons reaching the PMT.
The beam energy comes from the laser energy probe, which wasfactory calibrated to within 5% at 337 nm. The aperture uncertainty of 4% comes from geometrical survey of the chamber,which is used in the ray tracing program.
The ambient geomagnetic ﬁeld is 462 mG and is unshielded in
the current setup. By changing the orientation of the PMT, we
showed that it affects the point-to-point response map at the 20%
level but the average over the surface varies by only 4%.
The Rayleigh scattering angular distribution depends on thepolarization of the laser beam [32], so care was required to limit
any polarization effect. The effect can be strong because the PMT
only sees a Rayleigh scattering signal from the vertical componentof polarization: the horizontal component induces a dipole
moment oscillating perpendicular to the beam in the horizontal
plane, which cannot emit power to the PMT which is in the same
direction. On the other hand the energy probe reads the total
power regardless of polarization, so the fraction of power in thevertical direction must be under control. In our setup (Fig. 8), thelaser beam is ﬁrst linearly polarized at 453 and then passed
through a quartz l=4 waveplate to convert it to 100% circularpolarization. By rotating a linear polarizer in the beam, we
veriﬁed that the resulting horizontal and vertical components areequal to within better than 1%, which leads to a limit of 1% for thecorresponding systematic effect on the efﬁciency measurement.
Several analyses were performed to show that the scatteredphotons are coming from Rayleigh scattering and not othersources such as residual suspended dust. We checked for
expected scaling with gas density down to low pressure,symmetry of scattered light seen in forward and backward

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

9.4. Additional corrections
There are additional steps to obtain the detection efﬁciency of
DOMs from the PMT efﬁciency measurements, and these will bereported separately along with other studies on assembled DOMs.
Corrections include attenuation of light in the glass pressure
housing and the gel used for optical and mechanical coupling,
wavelength dependence in both the PMT sensitivity (quoted by
the manufacturer [16]) and the attenuation factors, and thegeometry of incident rays. These effects are included in a detailed
optical simulation of the DOMs [27,33] which will be compared tolaboratory measurements on assembled DOMs. A full detector
simulation can be used to combine the absolute efﬁciencies at
337 nm, the wavelength dependences, and the spectrum of lightreceived from neutrino interactions. Investigations of the combined effect show that IceCube detects signal photons in a broad
range centered on about 400 nm. These studies will be presented
elsewhere.
Our measurements were at 25 3 C, and some temperaturedependence can be expected. The manufacturer quotes a temperature coefﬁcient of 0:2%= 3 C for cathode sensitivity [16]. This is being
directly addressed by relative measurements of optical efﬁciency ofassembled DOMs at 45, 20 3 C and room temperature.
10. PMT linearity and saturation behavior
For most neutrino interactions expected in IceCube, any one
PMT will not detect more than a handful of photons. For such
events, and even when up to a few hundred are detected, the PMT
output is proportional to the number of photons detected.
However, some of the most interesting signal events would be
expected to deposit large amounts of energy within tens of metersof individual PMTs, and then the PMT response can be less thanproportional. Optimal reconstruction requires measuring thelinearity limit and modeling the nonlinear saturation behavior.
To study saturation behavior, PMTs were illuminated with LED
pulses of various durations and brightnesses. The duration of thelight pulses was varied from 3 ns to 1 ms, as measured with a fast PIN
photodiode (1 ns response time). A set of calibrated neutral density
ﬁlters was used to control the light level. For a given LED brightness,
illumination was ﬁrst measured by the PMT signal, using a ﬁlter
with sufﬁcient attenuation to allow linear operation of the PMT. The
observed signal was converted to a photoelectron rate and a total
number of photoelectrons (p.e.) using the SPE charge q0, determinedin a separate step. Then the illumination level was increased byusing different ﬁlters, with the new number of p.e. calculated fromthe ratio of ﬁlter attenuation coefﬁcients.
Fig. 10(a) shows the observed peak anode current I as afunction of the ideal peak current I0, deﬁned as the peak p.e. ratetimes the SPE charge. At gain 107, the PMT response is linear
within 10% up to currents of about 50 mA (31 p.e./ns), but
saturates completely at about 150 mA. Peak responses todifferent light pulse widths from 3 to 400 ns lie along a single
curve. The 3 and 20 ns width pulses were approximately Gaussianin shape, so the observation of identical peak response supports asaturation model where the observed current is a direct function

68

102
Ideal (linear)
Width 400 ns
I = Measured Current (mA)monitoring PMTs (see Fig. 8), and repeatability of measurements
after long time intervals.
The main systematic uncertainties in our method could be
reduced if desired, comparable to the current statistical precisionof about 2%. To accomplish this, one would calibrate the silicon
photodiode ‘‘energy meter’’ at the 1% level; measure the aperture
geometry more precisely; and provide good shielding from thegeomagnetic ﬁeld.

149

Width 20 ns
101

Width 3 ns
Fit

102

Gain 107
Gain 5×106

101

Gain 5×105
Gain 105
101

102

103

104

I0 = Ideal Current (mA)
Fig. 10. (a) PMT saturation curve for gain 107. The measured current is plottedagainst the instantaneous light level, deﬁned in terms of the current that would be
expected for an ideal (linear) device. Data points correspond to peak currents forthe indicated pulse widths. The ﬁt curve is given by Eq. (4), with parameterschosen optimally for this PMT (serial number SA2747). (b) Effect of PMT gain on
the saturation curve. Data points correspond to peak currents for 200 ns pulses for
PMT serial number AA0020. The curves show the ﬁtted parameterization, Eq. (5).

of the instantaneous illumination, with little cumulative effectfrom previous illumination. In particular the data are inconsistent
with models expressed in terms of total pulse charge, which wereused in some older versions of the IceCube simulation software.
The 400 ns pulses were approximately rectangular in shape andthe output current mirrored this shape well even in the saturation
region, again as expected for an instantaneous current saturation
model. Even long light pulses near saturation level show only
about 5% decline from 100 mA after 1 ms of steady illumination.
(Note this small history effect is independent of the transient gain
loss due to discharge of the dynode capacitors, which remains
below 1% for such a pulse.)
The same saturation behavior was found to apply regardless ofwhat part of the cathode was illuminated, even at 30 3 C, whichindicates that photocathode surface resistance [16] is notimportant on the relevant time scales.
The instantaneous current response is well parameterized by
the following:ln I0 ¼ ln I þ C

ðI=AÞBð1I=AÞ1=4:

ð4Þ

The parameters A, B and C differ substantially from one PMT toanother (Table 4), so the model should not be used to invert
observed saturated pulses unless each PMT is fully characterized.
Fig. 10(b) shows additional measurements at a range of lower
gains down to 105, relevant for IceTop DOMs. The model of Eq. (4)continues to apply over the full range if the parameters are scaled
approximately as powers of the gain, as shown by the curves
which are scaled by g  Gain=106 :AðgÞ ¼ 285g0:52 =ð1 þ g1=4 Þ2BðgÞ ¼ 13g0:18 =ð1 þ g1=4 Þ2CðgÞ ¼ 0:32g0:13 ð1þ g1=4 Þ2 :

ð5Þ

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

The given parameters apply to a single measured PMT, but similar
scaling behavior can be expected for other examples; as a ﬁrst
estimate one would adjust the leading coefﬁcients in eachparameter to match measurements at a particular gain, andretain the same scaling with gain. Note the good numericalbehavior of the scaling equations allows them to be used also for
estimates outside the given range of gain.
The instantaneous current model also helps understand how
the response to narrow light pulses (3 ns FWHM) broadens as
intensity increases (Fig. 11). With the light pulse strongly
attenuated (220 p.e.), the PMT output pulse width is similar to
the SPE response, about 10 ns. As more light is allowed to reachthe PMT (3700 p.e.), ﬁrst a gradual broadening occurs to about
20 ns width. This broadening follows from Eq. (4) because thepeak current is more attenuated than the rising and trailing edges.
At this point a tail is visible, along with a second peak delayed byabout 60 ns relative to the main peak. These are consistent withthe late photoelectron responses seen in SPE time resolution
measurements (Section 7), except that the relative sizes of main
peak and tail are altered by saturation in the main peak. At still
higher light levels (210,000 p.e.), the second tail peak iscomparable in size to the fully saturated main peak, and thetotal width is dominated by the combination of the two peaks.
The highest light level in Fig. 11 also exposes a small pre-pulse
30 ns before the main peak, as well as a substantial afterpulse
starting several hundred ns later (see Section 11). The pre-pulse isascribed to photoelectrons ejected from the ﬁrst dynode, and issomewhat exaggerated in Fig. 11 because the light source wasaimed at the center of the cathode with the dynode directly

behind. The individual quanta comprising the pre-pulse wereseparately studied using SPE-level illumination, and were foundto be between 1/10 and 1/20 of the SPE pulse size, occurring at
less than 1% of the SPE rate. The ratio between sizes of SPE pulses
and pre-pulse quanta is similar to the typical ﬁrst dynode gain
reported by the manufacturer [24]. Because individual pre-pulse
quanta are below threshold for triggering DOMs, they have asmall impact on event reconstruction. The combined pre-pulses
from many photons would only be observable for a large, narrow
light pulse (  5000 photons detected within 30 ns). Pulses
originating more than  25 m from a DOM would generally bebroader than this, due to scattering in the ice [7].
The saturation model (Eq. (4)) can be important for reconstruction of very high energy neutrinos that produce electromagnetic or hadronic showers. Ideally, reconstruction would rely
most heavily on the PMTs closest to a shower, because the lightpulse is broadened and attenuated as it travels through the ice[7]; however, these PMTs can be saturated for high energy events.
The energy where saturation effects become important can be
estimated by choosing a characteristic distance of 60 m, which isabout half the inter-string spacing. At this distance, simulations[20] show that a 600 TeV shower yields peak intensity of 30 p.e./ns, equivalent to the linearity limit of 50 mA. Above this energy,
signals in close PMTs require a correction for saturation. Above 10 PeV, many nearby PMTs are badly saturated and the shower
energy measurement must rely mostly on far-away PMTs.
However, even badly saturated PMTs measure the beginningand end of the pulse, which can be used to constrain the event
geometry.

Table 4
Saturation curve parameters for three PMT samples, as deﬁned for Eq. (4).

11. Afterpulses

PMT serial no.

A (mA)

B

C

AA0020
SA2747
SA2749

126
138
138

2.02
2.05
1.82

2.98
3.23
2.67

63 nsec

I = Measured Current (mA)

0

c
–40

–80

220 PEsb–120

3,700 PEs
210,000 PEs

a
0

200

400
600
Time (ns)

800

1000

Fig. 11. Average waveforms observed in PMT serial number SA2747 for 3 ns
(FWHM) light pulses with progressively higher intensity: (a) main peak; (b)secondary peak due to unusual electron trajectories and (c) pre-pulse.

As shown in Figs. 6 and 11, the prompt response to a lightpulse has a tail extending to about 100 ns. Afterpulses are seen in
the range of 300 ns to 11 ms. Such afterpulses are a common
feature of PMTs, and are attributed to ionization of residual gases
by electrons accelerated in the space between dynodes [34]. Ions
created in this way can be accelerated back to the photocathode,causing ejection of electrons which are subsequently ampliﬁed
like the original photoelectrons. Some ions strike one of thedynodes instead, but the corresponding ejecta are ampliﬁed muchless and could easily go undetected.
Afterpulse measurements were made at 25 3 C with LED pulsesof 40 ns width, using calibrated optical attenuators to control theintensity, as for the saturation measurements (Section 10). In abright LED ﬂash, many individual ions are created, and their
responses add up to an afterpulse waveform with well deﬁned
peaks and valleys (Fig. 12). The various peaks are believed tocorrespond to ions of different masses, according to theirindividual ﬂight times in the accelerating ﬁeld [34]. Prominent
afterpulse peaks for this PMT occur around 600 ns, 2 and 8 ms after
the main response peak. The peaks are fairly wide and no period isentirely devoid of afterpulses until after 11 ms.
The average afterpulse waveform grows almost linearly with
the ﬂash brightness even up to the highest intensity studied(4:4  106 p:e: in 40 ns), where the primary response is completely
saturated at  1000 p:e:=ns (Fig. 10). This suggests that observed
afterpulses arise primarily from ions generated in earlier stages ofthe multiplier, whose electron currents continue to rise evenwhen later stages have saturated.
Up to primary pulses of 1  106 p.e., the integral from 300 ns to11 ms corresponds to 0.06 SPE per primary photoelectron.
For dimmer ﬂashes, individual events have a small number ofafterpulse electrons. These appear as separate single afterpulses
distributed in time, with probability that can be approximately

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

an event with coincident arrival of one or more downgoing muons
from cosmic ray showers above the detector, which calls fordisentangling the hits originating from multiple tracks, andtherefore also the afterpulses. Multiple muons can also arise froma single shower, and when the resulting tracks are well separated
they can yield multiple hits. More intriguing is the possibility of nt
interactions which can create two showers of particles separated
by hundreds of meters [36]. In such a case some PMTs can see
pulses of light separated by a few microseconds, so effects ofafterpulses should be considered carefully. The late pulses
described in Section 7 should also be considered in these contexts.

0.0
c

–2.0
Measured Current (mA)d
3.0 x 103 PEs

b

–4.0

1.6 x 104 PEs–6.0

1.1 x 105 PEs

a

0
c

–40
–80

12. Summaryd
2.0 x 105 PEsb

1.0 x 106 PEs–120

4.4 x 106 PEs

a
0

5

10

Time (μs)
Fig. 12. PMT afterpulse waveforms for bright ﬂashes lasting 40 ns. Each curve isaveraged over many ﬂashes. The primary response (a) is off-scale and saturated atmost of these intensities. Brightness of ﬂashes is determined by the method ofSection 10, which is independent of PMT saturation effects. Prominent afterpulse
peaks are seen around (b) 600 ns, (c) 2 ms and (d) 8 ms after the primary response.
The afterpulse waveforms grow nearly linearly with ﬂash intensity up to the
maximum intensity measured. The PMT was operated at gain of 107, with theanode at 1326 V. Some variation in afterpulse waveforms is observed from one
PMT to another of the same type. Measurement of tails at very late times is slightly
affected by an AC coupling time constant of 80 ms.

predicted from the average waveforms of Fig. 12. Because
different ions are associated with different time ranges, andbecause some ions eject multiple electrons from the photocathode, each afterpulse delay range will be characterized by adifferent fundamental charge distribution. We have observed
corresponding peak charges from 1 SPE to 13 SPE, consistent witha recent more detailed study of individual ion afterpulses [35].
The above observations are from study of only a few PMT
samples, and the numbers quoted pertain to only one (serial
AA0020). Although quantitative differences are seen from one
sample to another, the information allows one to assess whether
afterpulses affect IceCube event reconstructions, and to limit
small systematic errors. If a particular physics analysis thenappears sensitive to afterpulses, a larger sample of PMTs would
have to be studied quantitatively to provide the necessary
corrections.
Given the small ratio of charge between afterpulse andprimary pulse, it can be expected that most IceCube analyses
will not be strongly sensitive to the details of afterpulses. Typical
IceCube events yield hits in each PMT that are spread over timesof a few hundred nanoseconds, well before the main part of theafterpulse distribution. For very high energy events (e.g. electronenergy 1 PeV in the deep ice), signals are likely to be seen by PMTs
500 m away where arrival times are dispersed over 2 ms (FWHM),
and then the afterpulse distribution becomes more relevant.
However, the main effect is a minor distortion of the late part ofthe pulse, which already has an intrinsically long tail due toscattering. Generally one does not lose much information bydisregarding details of the waveforms at late times.
However, some events can have multiple peaks in the photon
time distributions, and then a characterization of afterpulses canbe important for proper reconstruction. The most common case is

70

151

The R7081-02 PMT has been characterized and key ﬁndings
were discussed in the context of IceCube physics goals. We
observe a single-photoelectron time resolution of 2.0 ns averaged
over the face of the PMT. A small fraction of the pulses arrive
much later, with about 4% between 25 and 65 ns late. We also
observe prepulsing and afterpulsing, with afterpulsing occurring
up to 11 ms late. The single photoelectron charge spectrum is wellﬁt by a Gaussian corresponding to charge resolution near 30%,
plus a contribution at low charge which is represented by an
exponential. The dark rate was measured to be 300 Hz in thetemperature range 40 to 20 3 C. A new method for opticalsensitivity calibration has been demonstrated, which uses
Rayleigh scattering to scale from the intensity of a primary laser
beam to the much smaller number of photons reaching a target
PMT. Measurements of dark rate, single photon detection
efﬁciency, single photoelectron waveform and charge, time
resolution, large pulse response, and afterpulses will serve as
input for detailed simulation of IceCube physics events.

Acknowledgements
We acknowledge support from the following agencies: U.S.
National Science Foundation-Ofﬁce of Polar Program, U.S. National Science Foundation-Physics Division, University of Wisconsin Alumni Research Foundation, U.S. Department of Energy, andNational Energy Research Scientiﬁc Computing Center, theLouisiana Optical Network Initiative (LONI) grid computing
resources; Swedish Research Council, Swedish Polar Research
Secretariat, and Knut and Alice Wallenberg Foundation, Sweden;
German Ministry for Education and Research (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 technological research inindustry (IWT), Belgian Federal Science Policy Ofﬁce (Belspo);
Marsden Fund, New Zealand; Japan Society for the Promotion of
Science (JSPS); M. Ribordy acknowledges the support of the SNF(Switzerland); A. Kappes and A. Groß acknowledge support by the
EU Marie Curie OIF Program; J.P. Rodrigues acknowledge support
by the Capes Foundation, Ministry of Education of Brazil.
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[4] A. Karle for the IceCube Collaboration, IceCube, in: Proceedings of the 31st
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1–10 000 GeV, CERN Report 85–03, 1985.
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[7] M. Ackermann, et al., J. Geophys. Res. 11 (2006) D13203.
[8] D. Chirkin for the IceCube Collaboration, in: Proceedings of the 30th
International Cosmic Ray Conference, 3–11 July 2007, Merida, Yucatan,
Mexico, session HE1.5; in arXiv:0711.0353 [astro-ph], pp. 151–154.
[9] E. Andres, et al.AMANDA Collaboration, Astropart. Phys. 13 (2000) 1.
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[11] E. Middell, J. McCartin M. D’Agostino for the IceCube Collaboration, in:Proceedings of the 31st International Cosmic Ray Conference, 7–15 July 2009,
Lodz, Poland.
[12] T. Gaiser et al., IceCube Collaboration, IceTop Preliminary Design Document,
2003 /http://icecube.wisc.edu/S.
[13] A. Achterberg, et al.IceCube Collaboration, Astropart. Phys. 26 (2006) 155.
[14] R. Abbasi, et al.IceCube Collaboration, Nucl. Instr. and Meth. A 601 (2009) 294.
[15] Hamamatsu Corp., R7081-02 Photomultiplier Tube Data, 2003.
[16] Hamamatsu Corp., Photomultiplier Tubes: Basics and Applications, third ed., 2007.
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J.A. Nikkel, W.H. Lippincott, D.N. McKinsey, J. Instrum. 2 (2007) 1004;
H.O. Meyer, preprint arXiv:0805:0771v1 [nucl-ex], 2008.
[18] A.S. Dighe, M.Th. Keil, G.G. Raffelt, J. Cosmol. Astropart. Phys. 0306 (2003) 005.
[19] EMCO High Voltage Corporation, Sutter Creek, CA.

[20] J. Lundberg, et al., Nucl. Instr. and Meth. A 581 (2007) 619.
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[23] O.Ju. Smirnov, P. Lombardi, G. Ranucci, Instrum. Exp. Tech. 47 (2004) 69.
[24] Hamamatsu Corp., Personal communication.
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[26] A. Karle, Monte Carlo simulation of photon transport and detection in deep
ice: muons and cascades, in: Proceedings of the Workshop on Simulation andAnalysis Methods for Large Neutrino Telescopes, DESY 1998.
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72

Run118545-Event63733662
August 9th 2011
NPE 6.9928x104
Number of Optical Sensors 354

1

The slide of the first announcement on the detection of two PeV-Energy cosmic neutrino event candidates by IceCube at the Neutrino 2012 conference.
Presented by Ishihara of Chiba University representing the IceCube Collaboration.

2012 年ニュートリノ物理・宇宙物理国際会議において、二つの宇宙ニュートリノ事象候補検出を初公表したときの発表スライド。石原氏が IceCube 国際共同実験グループを代表して発表した。

MC

CC/NC interactions in the detector

Run119316-Event36556705
Jan 3rd 2012
NPE 9.628x104
Number of Optical Sensors 312

2 events / 672.7 days - background (atm. + conventional atm. ) expectation 0.14 events
preliminary p-value: 0.0094 (2.36

Two events passed the selection criteria

千葉大学研究室の冷凍庫の中に置かれた IceCube 実験用光電子増倍管。当時予算が限られていたため、支持台は大学構内のゴミ捨て場から拾ってきた材料で作った。この測定データから信号応答模型が作られ、IceCube実験検出器シミュレーター
に実装されることになる (2004年)。
The IceCube PMT set in the freezer box in the laboratory of the Chiba IceCube
group. The limited funding available at that time made us build the PMT
supporters with the free materials found in the university garbage pit. The
data from this measurement has built the signal response model implemented in
the IceCube detector simulation (2004).

PMT光電面をスキャンし、場所毎の光電変換効率を調べた。この結果も検出器シミュレーターに実装され使われている (2004年)。
The device to scan the photo-cathode surface for measurement of theposition-dependent photon detection efficiency. The knowledges from thismeasurement are included in the PMT simulation for the present IceCube MCdata generation (2004).

PMTを格納する耐圧ガラス球に被われたIceCube 光検出器モジュール(DOM)の検出効率の位置依存性を測定する装置 (2005年)。測定された角度依存性はIceCube モンテカル
ロシミュレーションの重要なパラメータのひとつである。
The scanning instrument for the IceCube optical detector modules (DOM) housing
the PMT within a pressure sphere.The obtained angular acceptance of the photon
conversion efficiency is among the key parameters in the IceCube detector
simulation (2005).

IceCube PMT/DOM の光子検出効率の絶対量を測定するためのセットアップ。
窒素ガスを密封したチェンバーとモニター用のPMTが手前にある。奥に見えるのがIceCube PMT が格納されている暗箱である(2005年)。
Our setup for measuring the PMT/DOM photon detection efficiency. A
pulsed 337nm laser beam is passed through a chamber containing purenitrogen gas put on the optical bench. You can see a black dark box
behind it housing the IceCube PMT/DOM to be calibrated (2005).

73

較正される IceCube PMT。位置決めのためのナトリウムレーザーの光が赤い点としてPMT表面に映っている(2005年)。
An IceCube PMT to be calibrated by the chamber. A red light spot from anatrium laser is seen in front of the PMT photo-cathode surface. Thisis the procedure for aligning the PMT and the beam axis in a straightline (2005).

南極点で凍えている吉田氏。IceTop 用の水タンクの開発を手伝っていた(2003年)。
Yoshida freezing at the South Pole. He was helping the R&D of
the water tank detector for the IceTop, the sub-component of
IceCube for measuring air showers (2003).

氷河内の光散乱を測定するチェンバーを製作し、南極に送った(2009年)。
The "Bubble Search Light", a chamber to measure the photon scattering
length in the polar ice, was built and shipped to the South Pole (2009).

南極にてチェンバーを埋設する石原氏(右端)と埋設チームのメンバー(2009年)。
Ishihara (far right) together with the deployment team at
the South Pole. Just before deploying the "Bubble SearchLight" down to the glacier ice (2009).

74

ICRC (宇宙線国際会議)最終日に総括講演を行っている吉田氏 (2005年)。ICRC
における総括講演者としては1999年以来2回めとなる登板であった。
Yoshida giving his Rapporteur talk at the ICRC (International Cosmic Ray
Conference) 2005. This was his 2nd appearance as a Rapporteur for the
conference since he had first worked on the same task in 1999.

ニュートリノ物理・宇宙物理国際会議で、IceCube 実験による高エネルギー宇宙
ニュートリノ事象候補の初検出を世界に公表する石原氏 (2012年)。
Ishihara, at the Neutrino 2012, making the first announcement to the worldon the IceCube's detection of two PeV-Energy neutrinos as the candidatesof cosmic neutrinos.

IUPAP (国際純粋・応用物理学連合)若手賞を受賞し、ICRC (宇宙線国際会議) 開
会式にてメダルと賞状を手にする石原氏 (2013年)。
Ishihara, who was awarded the IUPAP Young Scientist Prize, with the medal
and the certificate at the opening ceremony of the ICRC 2013 (2013).

リングイメージングチェレンコフ検出器国際ワークショップ(RICH)にて国際共同実験グループを代表して、IceCube 実験の最新成果について報告する間瀬氏 (2013年)。
Mase giving a talk on the latest results from IceCube, representing thecollaboration at the International Workshop on Ring Imaging Cherenkov Detectors(RICH) 2013.

75