PHYSICAL REVIEW D 67, 012003 共2003兲

Search for neutrino-induced cascades with the AMANDA detector
J. Ahrens,1 X. Bai,2 G. Barouch,3 S. W. Barwick,4 R. C. Bay,5 T. Becka,1 K.-H. Becker,6 D. Bertrand,7 F. Binon,7
A. Biron,8 S. Böser,8 J. Booth,4 O. Botner,9 A. Bouchta,8,* O. Bouhali,7 M. M. Boyce,3 T. Burgess,10 S. Carius,11 A. Chen,3D. Chirkin,5 J. Conrad,9 J. Cooley,3 C. G. S. Costa,7 D. F. Cowen,12 A. Davour,9 C. De Clercq,13 T. DeYoung,3,†
P. Desiati,3 J.-P. Dewulf,7 P. Doksus,3 P. Ekström,10 T. Feser,1 J.-M. Frère,7 T. K. Gaisser,2 M. Gaug,8 H. Geenen,6
A. Goldschmidt,14 A. Hallgren,9 F. Halzen,3 K. Hanson,3 R. Hardtke,3 T. Hauschildt,8 M. Hellwig,1 G. C. Hill,3 P. O. Hulth,10
K. Hultqvist,10 S. Hundertmark,10 J. Jacobsen,14 A. Karle,3 J. Kim,4 B. Koci,3 L. Köpke,1 M. Kowalski,8J. I. Lamoureux,14 H. Leich,8 M. Leuthold,8 P. Lindahl,11 I. Liubarsky,3 D. M. Lowder,5,‡ J. Madsen,15 P. Marciniewski,9H. S. Matis,14 C. P. McParland,14 T. Messarius,6 T. C. Miller,2,§ Y. Minaeva,10 P. Miočinović,5 P. C. Mock,4,储
R. Morse,3 T. Neunhöffer,1 P. Niessen,13 D. R. Nygren,14 H. Ogelman,3 Ph. Olbrechts,13 C. Pérez de los Heros,9 A. C. Pohl,11R. Porrata,4,¶ P. B. Price,5 G. T. Przybylski,14 K. Rawlins,3 C. Reed,4,** E. Resconi,8 W. Rhode,6 M. Ribordy,8
S. Richter,3 J. Rodrı́guez Martino,10 P. Romenesko,3 D. Ross,4 H.-G. Sander,1 K. Schinarakis,6 T. Schmidt,8 D. Schneider,3R. Schwarz,3 A. Silvestri,4 M. Solarz,5 G. M. Spiczak,15 C. Spiering,8 N. Starinsky,3,†† D. Steele,3 P. Steffen,8R. G. Stokstad,14 K.-H. Sulanke,8 I. Taboada,16,‡‡ L. Thollander,10 S. Tilav,2 M. Vander Donckt,7 W. Wagner,6 C. Walck,10
C. Weinheimer,1 C. H. Wiebusch,8,* C. Widemann,10 R. Wischnewski,8 H. Wissing,8 K. Woschnagg,5 W. Wu,4
G. Yodh,4 and S. Young41

共AMANDA Collaboration兲

Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
2
Bartol Research Institute, University of Delaware, Newark, Delaware 19716
3
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
4Department of Physics and Astronomy, University of California, Irvine, California 92697
5
Department of Physics, University of California, Berkeley, California 94720
6
Fachbereich 8 Physik, BUGH Wuppertal, D-42097 Wuppertal, Germany
7
Université Libre de Bruxelles, Science Faculty CP230, Boulevard du Triomphe, B-1050 Brussels, Belgium
8
DESY-Zeuthen, D-15735 Zeuthen, Germany
9
Division of High Energy Physics, Uppsala University, S-75121 Uppsala, Sweden
10
Department of Physics, Stockholm University, SCFAB, SE-10691 Stockholm, Sweden
11
Department of Technology, Kalmar University, S-39182 Kalmar, Sweden
12
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802
13
Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussel, Belgium
14
Lawrence Berkeley National Laboratory, Berkeley, California 94720
15
Physics Department, University of Wisconsin, River Falls, Wisconsin 54022
16
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104
共Received 27 June 2002; published 10 January 2003兲
We report on a search for electromagnetic and/or hadronic showers 共cascades兲 induced by a diffuse flux ofneutrinos with energies between 5 TeV and 300 TeV from extraterrestrial sources. Cascades may be producedby matter interactions of all flavors of neutrinos, and contained cascades have better energy resolution andafford better background rejection than throughgoing ␯ ␮ -induced muons. Data taken in 1997 with the
AMANDA detector were searched for events with a high-energy cascadelike signature. The observed eventsare consistent with expected backgrounds from atmospheric neutrinos and catastrophic energy losses fromatmospheric muons. Effective volumes for all flavors of neutrinos, which allow the calculation of limits for any*Present address: CERN, CH-1211, Genève 23, Switzerland.
†

Present address: Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064.
Present address: MontaVista Software, 1237 E. Arques Ave., Sunnyvale, CA 94085.
§
Present address: Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723.
储
Present address: Optical Networks Research, JDS Uniphase, 100 Willowbrook Rd., Freehold, NJ 07728-2879.
¶
Present address: L-174, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550.
**Present address: Dept. of Physics, Massachussetts Institute of Technology, Cambridge, MA 02139.
††
Present address: SNO Institute, Lively, ON, Canada P3Y 1M3.
‡‡
Present address: Dept. de Fı́sica, Universidad Simón Bolı́var, Apdo. Postal 89000, Caracas, Venezuela.
‡

0556-2821/2003/67共1兲/012003共10兲/$20.00

67 012003-1©2003 The American Physical Society

PHYSICAL REVIEW D 67, 012003 共2003兲

J. AHRENS et al.

neutrino flux model, are presented. The limit on cascades from a diffuse flux of ␯ e ⫹ ␯ ␮ ⫹ ␯ ␶ ⫹¯␯ e ⫹¯␯ ␮ ⫹¯␯ ␶ is
E 2 (d⌽/dE)⬍9.8⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 , assuming a neutrino flavor flux ratio of 1:1:1 at the detector.
The limit on cascades from a diffuse flux of ␯ e ⫹¯␯ e is E 2 (d⌽/dE)⬍6.5⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 , independent of the assumed neutrino flavor flux ratio.
DOI: 10.1103/PhysRevD.67.012003

PACS number共s兲: 14.60.Lm, 95.55.Vj, 95.85.Ry, 96.40.Tv

I. INTRODUCTION

Neutrinos interact principally via the weak force, posing a
detection challenge for neutrino telescopes but bestowing avaluable advantage on the field of neutrino astronomy: neutrino fluxes from astronomical sources are essentially unattenuated even over cosmological distances. In contrast, highenergy gamma rays are absorbed and/or scattered byintervening matter and photons, and high-energy cosmic-rays
are deflected by galactic and intergalactic magnetic fields
except at the highest energies (⬎1019 eV).
We present a search for the fully reconstructed light patterns created by electromagnetic or hadronic showers 共cascades兲 resulting from a diffuse flux of high-energy extraterrestrial neutrinos. We use data collected in 1997 from theAntarctic Muon and Neutrino Detector Array 共AMANDA兲
for this purpose. Demonstrating ␯ -induced cascade sensitivity is an important step for neutrino astronomy because thecascade channel probes all neutrino flavors, whereas themuon channel is primarily sensitive to charged current ␯ ␮and ¯␯ ␮ interactions. This is particularly relevant in view ofthe emerging understanding of neutrino oscillations 关1– 4兴, inwhich the flux of ␯ ␮ would be reduced by oscillations. 共The
detection of high-energy atmospheric muon neutrinos by
AMANDA has been demonstrated by the full reconstructionof Cherenkov light patterns produced by up-going muons关5–7兴.兲 Cascades also boast more accurate energy measurement and better separation from background, although they
suffer from worse angular resolution and reduced effective
volume relative to muons. Importantly, it is straightforward
to calibrate the cascade response of neutrino telescopes suchas AMANDA at lower energies through use of, e.g., in situ
light sources. Furthermore, cascades become increasingly
easier to identify and reconstruct as detector volumes getlarger, so the techniques presented here have relevance for
future analyses performed at larger detectors.
Electron neutrinos can produce cascades with no detectable track via the charged current 共CC兲 interaction and allneutrino flavors can produce cascades via the neutral current
共NC兲 interaction. Cascade-like events are also produced in ␯ ␶CC interactions when the resulting ␶ decays into an electron
共roughly 18% branching ratio兲 or into mesons 共roughly 64%
branching ratio兲 and the ␶ energy is below about 100 TeV, atwhich energy the ␶ decay length is less than 5 m, so that theshower produced by the neutrino interaction and the shower
produced by the ␶ decay cannot be spatially resolved by
AMANDA. The contribution of ␯ ␶ to the cascade channel
becomes important when flavor oscillations are taken into
account for extraterrestrial 关8 –10兴 and for atmospheric 关11兴
␯ -induced cascades. For extraterrestrial sources, current
knowledge of neutrino oscillations suggests a detected neu-trino flavor flux ratio of ␯ e : ␯ ␮ : ␯ ␶ ::1:1:1 following an expected flux ratio of 1:2:0 at the source.
The total light output of an electromagnetic cascade isapproximately 108 photons/TeV in ice. Hadronic cascades
have a light yield about 20% lower 关12兴. An electromagnetic
cascade develops in a cylinder of about 10–15 cm in radius
共Molière radius兲 and several meters in length 共about 8.5 mfrom the vertex of a 100 TeV cascade, essentially all charged
particles are below the critical energy兲. Hadronic cascades
have longer longitudinal developments and larger Molièreradii. As a sparsely instrumented detector, AMANDA is insensitive to the topological differences between electromagnetic and hadronic cascades. Since the NC interaction has alower cross section and results in a deposition of less energy
than the CC interaction, and since we assume a steeply falling neutrino energy spectrum, at any given energy a verysmall fraction of the ␯ e events are due to NC interactions.
Hence their impact on the cascade energy resolution is small,and the energy spectrum of reconstructed cascades closely
follows that of the CC ␯ e energy spectrum.
In this paper, we present limits on the diffuse fluxes of( ␯ e ⫹ ␯ ␮ ⫹ ␯ ␶ ⫹¯␯ e ⫹¯␯ ␮ ⫹¯␯ ␶ ) and ( ␯ e ⫹¯␯ e ), assuming a customary E ⫺2 power law spectrum at the source. These limits
are based on the observation of no events consistent with adiffuse flux of high-energy extraterrestrial neutrinos. We alsopresent effective volumes for all neutrino flavors to facilitate
the calculation of a limit for any flux model. 共A search for
up-going muons produced by a ␯ ␮ extraterrestrial diffuse
flux is presently being conducted and preliminary results
have been reported in 关13兴.兲
II. THE AMANDA-B10 DETECTOR

The data used in this work were taken with the
AMANDA-B10 detector in 1997. AMANDA-B10 关6,7,14兴
was commissioned in 1997 with a total of 302 optical modules 共OMs兲 arranged on 10 strings, at depths between 1500m and 2000 m below the surface of the ice at the South Pole.
The strings are arranged in two concentric circles 35 m and
60 m in radius, with one string at the center. The OMs in the
inner four 共outer six兲 strings have a 20 m 共10 m兲 verticalseparation. Each OM contains a 20 cm photo-multiplier tube
共PMT兲 in a spherical pressure vessel. Coaxial cables in the
inner four strings and twisted pair cables in the outer six
strings provide high voltage to the PMTs and simultaneouslytransmit their signals to the electronics housed on the surface. The detector is triggered using a majority condition inwhich an event is recorded if more than 16 modules have asignal 共i.e., were ‘‘hit’’兲 in a 2 ␮ s time window. A total of
1.05⫻109 events were recorded during an effective live timeof 130.1 days.

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The optical properties of the ice have been studied with insitu light sources and with atmospheric muons. These studies
have shown that ice at the South Pole is not perfectly homogeneous, but rather consists of horizontal layers corresponding to global climatological conditions in the past, such as
ice ages. These layers lead to a modulation of the absorption
and effective scattering lengths as a function of depth 关15兴.
Optical properties are also modified by the presence of drillhole bubbles which are created during the drilling and deployment processes.

provides a significant improvement over the center of gravity
in the estimation of the vertex position and time of the cascade. The estimate will be further improved by the multiphotoelectron reconstruction descrived below.
B. Multi-photoelectron vertex position and time reconstruction

The single photoelectron likelihood can be refined by taking into account that the time measured in each PMT is thetime of the first photon to be observed. If a PMT receives N
photons, the probability of measuring a time residual, t res ,and the associated likelihood function are

III. METHODS FOR CASCADE RECONSTRUCTION

Simple reconstruction algorithms are initially applied tothe data. These methods are used to reduce the data sample
size and to seed more sophisticated reconstruction algorithms, while maintaining high passing rates for simulated
signal events. For cascades, the mean position of the hit
OMs, or center of gravity, is used as the first guess of theposition. In order to efficiently reject muons, they too arereconstructed, beginning with a first guess track fit called theline fit 关16兴. The line fit is an algorithm that assumes that hits
can be projected onto a line, and that the particle which
produced the hits travels with a velocity vជ line and has a startN
ing point rជ 0 . The fit minimizes the quantity 兺 hits(rជ i ⫺rជ 0i⫽1⫺ vជ line•t i ) 2 as a function of rជ 0 and vជ line , where Nhits is thenumber of hits in the event. These procedures are describedin more detail elsewhere 关17,18兴.
After calculating the first guesses, three maximum likelihood methods are used consecutively to reconstruct precisely
the cascade vertex position, time, energy and direction.
These methods are described below.

p 共 N,t res ,d 兲 ⫽Np 共 t res ,d 兲

⬁

t res

dt ⬘ p 共 t ⬘ ,d 兲

冊

N⫺1

共2兲

N hitsLxmpe
ជ ,t ⫽

兿 p 共 N,t resi ,d i 兲

i⫽0

共3兲

where the ‘‘mpe’’ label indicates that Lxmpe
ជ ,t describes multiphotoelectron hits. In AMANDA we use the measured pulse
amplitude as an estimator for N.
The maximization of Lxmpe
ជ ,t is used to estimate the mostជlikely vertex position x and time t of a cascade. The multiphotoelectron vertex reconstruction uses the maximization ofspe
Lxជ ,t to seed initial values of cascade vertex position andtime.
C. Energy and direction reconstruction

Cascade energy and direction are reconstructed using alikelihood function assembled from the probabilities of an
OM being hit or remaining unhit assuming a cascade hypothesis:
Hit OMs

A. Single photoelectron vertex position and time reconstruction

The cascade vertex position and creation time are reconstructed using a maximum likelihood function that takes into
account the Cherenkov emission, absorption and scatteringof light. This vertex information is required for rejecting potential backgrounds and for subsequent fits for energy anddirection. This procedure is quite similar to the algorithms
used for muon fitting 关17兴. A more comprehensive description of the different cascade reconstruction methods can befound in 关18 –20兴.
We use a likelihood function having the form冉冕LE,n̂ ⫽

兿i⫽0Unhit OMs

P Hit共 d i ,E,n̂ 兲兿i⫽0P Unhit共 d i ,E,n̂ 兲 . 共4兲

Maximization of LE,n̂ provides the most likely value of energy E and direction n̂ of a cascade. Note that in principle
this procedure also allows for the reconstruction of position
共but not time兲 of a cascade. Monte Carlo studies have shown,however, that the position resolution obtained by maximizing
mpeLE,n̂ is not as good as that obtained with Lxspe
ជ ,t or Lxជ ,t .
IV. DETECTOR RESPONSE TO CASCADES

N hitsLxspe
ជ ,t ⫽

兿 p 共 t resi ,d i 兲 ,

i⫽0

共1兲

where t res⫽t hit⫺t Cher is the difference between observed hit
time and expected time for Cherenkov emission without
scattering—the time residual—and p(t res ,d) is the probability of observing a photon at a time residual t res at a distancespe
d from the emitter. The label ‘‘spe’’ indicates that Lxជ ,t assumes all hits are due to single photoelectrons.
The probability p(t res ,d) was generated by parametrizing
simulations of light propagation in ice. The product in Eq.
共1兲 is calculated using all hit OMs. The maximization of Lxspe
ជ ,tIn the absence of a tagged source of high-energy neutrinoinduced cascades, to understand the response of the detector
we rely on in situ light sources, catastrophic energy losses by
down-going cosmic-ray muons, and Monte Carlo simulations. The successful reconstruction of these data demonstrate detector sensitivity to cascade signals.
A. Pulsed laser

A pulsed laser operating at 532 nm on the surface is used
to send light through optical fibers to diffuser balls embedded in the ice close to almost every OM in the detector. A
comparison of Monte Carlo and experimental data for these012003-3

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FIG. 1. The figure shows four plots with results of the reconstruction of pulsed laser data 共solid兲 and simulation 共dashed兲 with the diffuserball next to OM 69 共situated near the center of the detector兲. The differences between simulated and reconstructed x and z components of thempeposition, the speed of the line fit, v line , and the reduced likelihood parameter, L xជ ,t , are shown. The vertical scale for all four plots isarbitrary. The position of the OM is known with about 1 m precision 关21兴, so there is no discrepancy in the reconstructed ⌬z plot. The
discrepancy in the likelihood parameter plot arises due to the simplified ice model used for the pulsed laser.

in situ light sources deepens our understanding of reconstruction performance and detector signal sensitivity. The
photon intensity that can be produced at each diffuser ball is
not known a priori, so we force the number of hit channels
in experimental and simulated pulsed laser data to match.
Thus, the simulations predict that the laser produces pulses
in the ice comprising 5⫻107 ⫺1⫻109 photons 共corresponding to a maximum cascade energy of roughly 10 TeV兲. The
laser pulses are roughly 10 ns wide, short enough to mimic
the time structure of true cascades.
Although highly useful as a cascade calibration source,
the pulsed laser system has some minor drawbacks. The diffuser ball light output is expected to be isotropic, so the laser
data does not provide information about the angular responseof the detector to cascades. The laser produces light at ␭
⫽532 nm and at this wavelength the optical ice propertiesare different from those at Cherenkov radiation wavelengths.
The effective scattering length at 532 nm is 18 –30 m anddepends on depth. The absorption length at 532 nm is 25 m

and independent of depth 关15兴 共at the shorter wavelengths
characteristic of Cherenkov radiation the absorption length isabout 100 m兲.
Independent data sets taken with diffuser balls in a varietyof locations are reconstructed with the first guesses and withthe time-position reconstruction algorithm described above.
The position resolution is about 1 m in the z dimension andabout 2 m the in x and y. It is better in z due to closer OM
spacing in that dimension.
The pulsed laser simulation uses a simplified opticalmodel of ice properties: the drill-hole bubbles are taken into
account, but no depth dependence is used for the scattering
length. In spite of this simplification, the vertex resolution of
the pulsed laser data agrees well with simulations, showingthat the detector can be used to reconstruct the position ofcontained point-like events. 共Contained events are defined as
events whose reconstructed vertex lies within a right cylinderof height 400 m and radius 60 m, centered on the
AMANDA-B10 detector and encapsulated by it.兲 Figure 1

TABLE I. Selection criteria used in the search for high-energy ␯ -induced cascades with AMANDA-B10.
The number of events left after applying each selection criterion to experimental data and backgroundsimulations of atmospheric ␮ , ␯ e and ␯ ␮ are shown. We simulated 20.3 days of atmospheric ␮ data, and130.1 days of atmospheric ␯ e and ␯ ␮ . Signal simulation is also shown for ␯ l ⫹¯␯ l and ␯ e ⫹¯␯ e assuming E ⫺2
spectra, a flux of 1⫻10⫺4 GeV⫺1 cm⫺2 s⫺1 sr⫺1 .
Selection criteria

Expt. data

Atm ␮

Atm ␯ eAtm ␯ ␮␯ l ⫹¯␯ l␯ e ⫹¯␯ e

1.05⫻109

1.51⫻108

369.9

245.5

12446

12150

1
2
3
4
5

Trigger
N big TOT⭓6v line⬍0.12 or N hits⭓75
␭ 1 /␭ 3 ⬎0.35
spe⭓8 or N hits⭓75
N dir
spe
L xជ ,t ⬍7.4 or N hits⭓75

5.57⫻1061.12⫻106

51.1

40.4

2727

3424

6
7
8
9
10
11

L xជ ,t ⬍7.1
mpe
N dir
⭓12
␪ ␮ ⬎80°
Slices in z ccos(␪c)⬍⫺0.6
E c vs ␳ mpe

1.50⫻1061.26⫻1063.62⫻105
1.48⫻105675
02.03⫻105
1.14⫻105
2.47⫻104
1.19⫻104
84
0

38.2
32.1
22.5
10.6
1.3
0.01

30.7
26.2
18.5
8.5
1.0
0.01

2128
1909
1105
528
106
28.7

2818
2520
1676
711
156
43

mpe

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number of hits produced by the brightest cascade in simulated events, and on a visual study of these events, we haveconfirmed that after applying these selection criteria the remaining events are indeed cascade-like.
Figure 2 shows the energy spectra of muon energy losses
for experimental data and simulated atmospheric muons. The
experimental and simulated data agree reasonably well, but
not perfectly. The difference is discussed in Sec. VI.
C. Monte Carlo prediction for neutrino-induced
cascade reconstruction

FIG. 2. Energy spectra of reconstructed atmospheric muon energy losses for experimental data and standard simulated muon
background after application of selection criteria 1–9 from Table I.
Agreement between simulation and experimental data depends on a
combination of the simulated ice properties and the OM angular andabsolute sensitivity. These effects have been taken into account in
the calculation of systematic uncertainties in Sec. VI.

shows the results of the reconstruction of pulsed laser dataand simulation.
B. Catastrophic muon energy losses

The vast majority of the events recorded by AMANDA
are down-going muons induced by cosmic-ray air showers.
This background has been simulated with the CORSIKA program 关22兴 using the average winter air density profile at theSouth Pole and the QGSJET hadronic model 关23兴 option. The
cosmic-ray composition is taken from 关24兴. The propagationof muons through ice is simulated with the program MUDEDX
关25,26兴. Optical properties of the ice, including depth dependence and drill-hole bubbles, are also simulated.
From the large sample of atmospheric muons it is possible
to extract a subset of cascade-like events in which the majority of the recorded hits come from catastrophic, localizedenergy loss of the muon 共e.g., a bright bremsstrahlung兲. The
extraction of these events is achieved using criteria 1–9 from
Table I, i.e., we do not require these events to reconstruct as
up-going cascades. 共We do, however, still reject obvious
down-going muons via criterion number 8.兲 Based on the

To study the performance of the reconstruction algorithms
we simulated a flux of ␯ e ⫹¯␯ e following an E ⫺2 power law
spectrum. Neutrinos from astrophysical sources are expected
to have a hard spectrum, reflecting the processes in the cosmic accelerators that generate them. Earth absorption and
NC scattering are taken into account in the simulation. The‘‘preliminary reference Earth model’’ is used to calculate theEarth’s density profile 关27兴. We calculate differential crosssections using CTEQ5 following Gandhi et al. 关28兴. For ␯ ␶interactions, the simulation of the ␶ decay uses TAUOLA 关29–
31兴.
Neutrino-induced cascades are reconstructed following
the procedure described in Sec. III. Position, zenith angle
and energy resolutions for a flux of ␯ e ⫹¯␯ e are calculatedusing the difference distributions shown in Fig. 3. The position resolution is roughly 4 m in the z dimension and 5.5 m
in x and y for contained cascades. 共Note that position resolution obtained with the pulsed laser is better than that predicted for Cherenkov light because optical ice properties are
more favorable at the longer wavelength.兲 The reconstructed
position is biased in the direction of the cascade, but since
the mean of this shift is only about 2 m for contained cascades it has a negligible impact on the final result. Zenith
angle resolution is 25° –30° depending on the cascade energy.
The energy reconstruction has a resolution of 0.12–0.20
in log10E for contained cascades in the range 1 TeV–100
TeV, increasing as a function of cascade energy. Energy reconstruction of contained cascades is possible from approximately 50 GeV 共the minimum energy cascade which can
trigger the detector兲 to about 100 TeV. At energies higher
than 100 TeV all, or almost all, of the OMs are hit and thus
energy reconstruction by the minimization of Eq. 共4兲 is not

FIG. 3. The four plots show the difference between simulated and reconstructed vertex position, energy and direction of cascades. The
monoenergetic cascades have E⫽10 TeV and are contained within the detector. Vertical scale for all four plots is arbitrary.
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possible. 共Such high-energy events would, however, certainly be identifiable, and probably they can be reconstructedby other techniques.兲
V. ANALYSIS
A. Filter

The first step in the analysis is to apply an initial set of
selection criteria, here called the ‘‘filter,’’ which results in a
reduction of the data sample size by more than two orders ofmagnitude. The filter first removes spurious hits arising fromelectronic and PMT noise. It then uses the fast reconstruction
algorithms described earlier, a simple energy estimator, andtopological characteristics of the hit pattern to select potential signal events. The various filter steps were tuned to rejecta simulated background of down-going cosmic-ray muons.
After the filter has been applied, hits likely to have comefrom cross-talk are removed, as explained below. Then each
event is reconstructed twice, first with a cascade hypothesis
and then with a muon hypothesis. Several selection criteria
are then applied to the data based on the results of the reconstruction.
Atmospheric ␯ e and ␯ ␮ neutrinos are simulated according
to the flux calculated by Lipari 关32兴. Contributions to cascades from both atmospheric ␯ e 共CC and NC interactions兲and ␯ ␮ 共NC interactions兲 are taken into account. In the energy range relevant to this analysis (E⬎5 TeV), neutrino
oscillations are not important in the simulation of atmospheric neutrinos.
B. Removal of electronic cross-talk

Electronic cross-talk is present in the twisted pair cables
used for strings 5–10. Spurious hits arising from cross-talk
can degrade the reconstruction quality. Cross-talk is not included in the simulations, so its removal is an important facetof this analysis.
We generate a detector-wide map of the cross-talk using
the pulsed laser. For each OM in strings 5–10, pulsed laser
data are taken in which only the PMT in the OM near thelaser diffuser ball has its high voltage enabled. Any hit in the
flashed OM is thus known to be due to light and any hit inany other OM is known to be due to cross-talk. The crosstalk map identifies the pairs of cross-talk-inducing and crosstalk-induced OMs as well as the correlation in time and amplitude of real and cross-talk hits. The map shows that crosstalk occurs for OMs in the same string that are close
neighbors or for OMs in the same string that are separated by
150–200 m. The origin of cross-talk is correlated with therelative positioning of individual electrical cables within thestring 关33兴.
Cross-talk hits may also be characterized by narrowness
共small time over threshold or ‘‘TOT’’兲 coupled with unexpectedly large amplitude. Cross-talk-induced and lightinduced hits lie in different regions of the amplitude vs TOT
space and may therefore be separated from one another. Figure 4 shows the amplitude vs TOT distributions for bothtypes of hits.

FIG. 4. Amplitude vs time over threshold 共TOT兲 distribution forhits on OM 149 due to light and cross-talk. The data shown to theright of the solid curve are generated using the pulsed laser with
only the high voltage for the PMT in OM 149 enabled 共all other
PMTs had their high voltage disabled兲. This region of the plot therefore contains hits created by light. The data shown to the left of thesolid curve are also generated using the pulsed laser, but with adiffuser ball located 200 m above OM 149, close to OM 129, in thesame string as OM 149. Only OM 129 had its high voltage enabled.
This region of the plot therefore contains hits in OM 149 due tocross-talk. Hits are removed from an event if they lie to the left ofthe dashed curve or if they have a TOT smaller than 125 ns 共indicated by the dashed line兲.

The cross-talk map and the amplitude vs TOT information
are both used to remove cross-talk from the experimental
data.
C. Selection criteria

Table I lists the selection criteria and the passing rates forexperimental data and the various samples of Monte Carlocalculations used in this analysis. Selection criteria whichhave not already been described in Sec. III are described
below, followed by a physical justification for each criterion.
The ratio of the smallest to the largest eigenvalues of thetensor of inertia of the position of the hits, ␭ 1 /␭ 3 or sphericity, is used to classify events.1 Small values of the sphericity correspond to hits located along a narrow cylinder, as
expected for a muon. Values of the sphericity close to unity
correspond to a spherical distribution of the hits, as expected
for contained cascades.
The dispersive nature of the ice and of the cables thattransmit the electrical signals from the OMs to the electronics on the surface render sharp signals in the ice into significantly broader pulses at the surface. For this reason, counting
the number of OMs with large TOT, N big TOT , gives a roughestimate of the energy of the event. For this analysis a TOT
is considered large if it exceeds the value estimated fromMonte Carlo simulations to correspond to one photoelectron
by at least a factor of 1.5. A contained cascade with 300 GeV
1
To calculate a tensor of inertia in this context, a unit mass ishypothesized at each hit OM position.

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FIG. 5. Normalized distribution of the reduced likelihood pampe
rameter L xជ ,t for experimental data 共solid line兲, background atmospheric ␮ simulation 共dashed line兲, ␯ e simulation assuming an E ⫺2
power law spectrum 共dotted line兲 and contained ␯ e simulation assuming an E ⫺2 power law spectrum 共dotted-dashed line兲. Contained events have their vertices in a cylinder 400 m in height and
60 m in radius, roughly matching the detector dimensions. Selection
criteria 1–5 from the same table have already been applied to all thesamples shown. The arrow indicates the region removed by cut 6from Table I.

of energy corresponds roughly to N big TOT⫽6.
The quality of the likelihood reconstruction is determinedfrom the reduced likelihood parameter, defined by L⫽⫺logL/(N hits⫺N fit), where N fit is the number of fitted parameters. Lower values of L correspond to better reconstruction quality.
A hit is considered direct if the time residual is between⫺15 ns and 75 ns. The number of direct hits, N dir , is anothermeasure of the quality of the reconstruction. Both the single
and multi-photoelectron position-time reconstruction report
the number of direct hits.
Criteria 1–5 of Table I correspond to the filter and thesecriteria must be satisfied by all events in the analysis. The cut
on N big TOT selects high-energy events, and the cut on thesphericity selects events in which the hit topology is cascadelike. The cut on the speed of the line fit, v line , removes easily
identified down-going muons. As shown in Fig. 5 and Fig. 6,
cuts on the likelihood parameter 共criterion 6兲 and the numberof direct hits 共criterion 7兲 are used to eliminate non-cascadelike events and preserve cascade-like events with good reconstruction quality. In addition to the filter criteria, angularcuts 共criteria 8 and 10兲 are used to reduce clear muon-likeevents and to select up-going cascade-like events, and criterion 11 selects high-energy events within a given distancefrom the vertical axis of the detector, where E c is the reconstructed cascade energy using Eqs. 共3兲 and 共4兲, and ␳ mpe⫽ 冑(x mpe) 2 ⫹(y mpe) 2 . 共Criterion 9 is discussed in detail below.兲
The filter was developed based strictly on the predictionsof the signal and background Monte Carlo simulations. As
more and more cuts were applied after the filter, it was foundthat the experimental data and simulations disagreed in the
shape of the z component of the reconstructed cascade posi-

FIG. 6. Normalized distribution of direct hits for experimental
data 共solid line兲, background atmospheric ␮ simulation 共dashedline兲, ␯ e simulation assuming an E ⫺2 power law spectrum 共dottedline兲 and contained ␯ e simulation assuming an E ⫺2 power law spectrum 共dotted-dashed line兲. Contained events have their vertices in acylinder 400 m in height and 60 m in radius, roughly matching thedetector dimensions. Selection criteria 1–5 from the same table
have already been applied to all the samples shown. The arrow
indicates the region removed by cut 7 from Table I.

tion and in the reconstructed cascade direction. Inadequately
simulated or unsimulated detector instrumentals, such as optical properties of the ice and cross-talk, contribute to thisdisagreement. Restricting the regions of the detector used inthis analysis reduces the effective volume by more than afactor of two, but restores the agreement between experimental data and simulations. Moreover, the disagreement is alsopresent in the reconstructed cascade direction. Only the regions of the detector that are accepted, show agreement in
the reconstructed cascade direction. Events are accepted only
if their reconstructed vertices satisfy selection criterion number 9: ⫺80 m⭐z c ⭐⫺40 m or 40 m⭐z c ⭐160 m with respect to the center of the detector 共located at 1730 m below
the surface兲.
VI. SYSTEMATIC UNCERTAINTIESThere are several uncertainties inherent in estimating thedetector sensitivity to high-energy neutrino-induced cascades. First, the detection medium is a natural material
共South Pole ice兲 whose properties are not precisely known.
Second, there are no sufficiently powerful accelerator-basedsources of neutrinos available for use as calibration beams.
Consequently, the understanding of the detector sensitivity isachieved using down-going atmospheric muons, in situ lightsources and Monte Carlo simulations.
To estimate the systematic uncertainty due to imprecise
knowledge of the optical properties of the ice, simulations
have been performed using the least and the most transparent
ice that we have measured at AMANDA depths. The cascadesensitivity is modified by 20% using either extreme model ofthe optical properties. Uncertainties in the bubble density inthe drill-hole ice translate to uncertainties in the OM angularsensitivity. Monte Carlo simulations with increased bubble
density in the drill-hole ice degrade the cascade sensitivity

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by 9%. The absolute sensitivity of the OMs is also uncertain
at the level of 40%. Monte Carlo simulations with alteredabsolute OM sensitivity modifies the cascade sensitivity by
5%. This dependence is weak due to the high N hits requirement imposed by this analysis. 共The dependence is muchstronger at earlier stages of the analysis, where the average
N hits is much lower. For example, before the filter is applieda variation in absolute OM sensitivity of 40% results in a
modification of the cascade sensitivity by roughly 35%.兲
Cross-talk can reduce the sensitivity of the detector tohigh-energy neutrino-induced cascades. Events for whichcross-talk is not fully removed are typically misreconstructed and are therefore unlikely to have sufficientquality to pass our selection criteria. The pulsed laser data isused to estimate the cascade sensitivity loss due to cross-talkfor different locations in the detector. These studies indicatethat the sensitivity is degraded by 7% due to cross-talk. 共This
7% degradation is applied directly to the limit and not treatedas a systematic uncertainty.兲 Related to cross-talk is the uncertainty in the limits due to using slices in z c . Changing
each boundary of the slices by the position resolution in z
modifies the cascade sensitivity by 4%.
Uncertainties in the limits due to neutrino-nucleon crosssections, total cascade light output, and cascade longitudinaldevelopment have also been estimated using Monte Carlosimulations. For each of these cases the cascade sensitivity is
modified by ⬍5%.
The systematic uncertainties discussed so far are added inquadrature, giving an overall systematic uncertainty on thesensitivity of 25%. We follow the procedure described in关34,35兴 to determine how to modify the final limit in light of

E2

d⌽
⫽
dE

TN A ␳ ice

兺l

fl

冕

d⌽
⬍9.8⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 .
dE

VII. RESULTS

The analysis is applied to simulated samples of atmospheric ␯ e and ␯ ␮ background, high-energy neutrino signal
共all flavors兲, and atmospheric muons, and to the 1997 experimental data set. In the experimental data zero events arefound. The simulation of atmospheric ␯ e predicts 0.01
events, and the simulation of atmospheric ␯ ␮ predicts 0.01
events from NC interactions 共both these numbers have beenrounded up from distinct smaller values兲. Zero events arefound in the simulated atmospheric muon sample after all
cuts. A limit on the flux of neutrinos assuming an E ⫺2 powerlaw spectrum is set using the following formula:

N 90%
l
l
E ⫺2 ␰ l 共 E, ␪ 兲 ␴ tot
共 E 兲 V eff
共 E, ␪ 兲 d⍀dEwhere l is the neutrino flavor, E the neutrino energy, ␪ theneutrino zenith angle, N 90% ⫽2.62 determined using the unified Feldman-Cousins procedure 关36兴 with a correction applied for the estimated 25% systematic uncertainty 关34,35兴, T
the live time 共130.1 days兲, N A Avogadro’s number, ␳ ice thel(E) the neutrino cross section 关28兴,
density of ice, ␴ totl
V eff(E, ␪ ) the effective volume of the detector 共see Table II兲,f l the fraction of the total neutrino flux comprised by theneutrino flavor l, and ␰ l (E, ␪ ) a function that corrects the flux
for Earth absorption and NC scattering. The integration of
Eq. 共5兲 has been done for neutrino energies between 5 TeV
and 300 TeV.
The 90% C.L. limit on the diffuse flux of ␯ e ⫹ ␯ ␮ ⫹ ␯ ␶¯⫹ ␯ e ⫹¯␯ ␮ ⫹¯␯ ␶ for neutrino energies between 5 TeV and 300
TeV, assuming a neutrino flux ratio of 1:1:1 at the detector, is
E2

this systematic uncertainty, assuming that the uncertainties
are of a Gaussian nature.
The spectrum of cascade-like events produced by downgoing muons is shown in Fig. 2 共see also Sec. IV B兲. Standard simulations as well as simulations with modified ice
properties and OM angular and absolute sensitivities havebeen performed. The disagreement between experiment andsimulations may be explained by the uncertainties in theknowledge of the optical properties of ice, the OM sensitivity, the cosmic-ray spectrum and the rate of muon energy
losses. From Fig. 2 it can be seen that reasonable agreement
between experiment and simulations is restored by shifting
the energy scale by up to 0.2 in log10E. This uncertainty inthe energy scale results in an uncertainty on the sensitivity ofless than 25%. This uncertainty is not independent of theother sources of systematic uncertainty that we have studied.
It demonstrates, however, that the overall systematic uncertainty has not been grossly under- or overestimated.

共6兲

共5兲

The 90% C.L. limit on the diffuse flux of ␯ e ⫹¯␯ e for neutrinoenergies between 5 TeV and 300 TeV isE2d⌽⬍6.5⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 .
dE

共7兲

The latter limit is independent of the assumed neutrino flux
ratio. The limits without incorporating the effects of systematic uncertainties are 9.1⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 and 6.1⫺1⫻10⫺6 GeV cm⫺2 s⫺1sr , respectively. 关Note that since thelimit in Eq. 共6兲 is on the sum of the fluxes of all neutrino
flavors, and the limit in Eq. 共7兲 is on an individual flavor, theformer limit should be divided by a factor of three to compare it properly to the latter.兴
Our results together with other limits on the flux of diffuse neutrinos are shown in Fig. 8. Since recent results fromother low energy neutrino experiments 关1– 4兴 indicate thathigh-energy cosmological neutrinos will have a neutrino fla-

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TABLE II. Effective volume, in units of 10⫺3 km3 , for all neutrino flavors as a function of energy andzenith angle after all the selection criteria have been applied. Uncertainties are statistical only.

␯e

¯␯ e

␯␮

¯␯ ␮

␯␶

¯␯ ␶

3.0–10.0 TeV

10.0–30 TeV

30–100 TeV

100–300 TeV⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2⫺0.2⬍cos ␪⬍0.2

0.80⫾0.05
0.40⫾0.03
0.08⫾0.01

1.85⫾0.10
0.85⫾0.07
0.22⫾0.02

1.87⫾0.15
1.10⫾0.10
0.36⫾0.05

1.37⫾0.20
0.72⫾0.10
0.31⫾0.07⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2

0.82⫾0.05
0.42⫾0.03

1.67⫾0.12
0.77⫾0.07

1.85⫾0.10
0.92⫾0.07

1.60⫾0.15
0.74⫾0.10⫺0.2⬍cos ␪⬍0.2

0.09⫾0.01

0.20⫾0.02

0.35⫾0.05

0.30⫾0.07⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2⫺0.2⬍cos ␪⬍0.2

0.08⫾0.02
0.05⫾0.01

0.35⫾0.05
0.25⫾0.03

0.87⫾0.1
0.70⫾0.10

1.27⫾0.15
1.60⫾0.10
0.05⫾0.01⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2

0.12⫾0.02
0.05⫾0.01

0.34⫾0.05
0.25⫾0.03

0.70⫾0.05
0.70⫾0.1

1.17⫾0.15
0.14⫾0.01⫺0.2⬍cos ␪⬍0.2

0.03⫾0.01⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2⫺0.2⬍cos ␪⬍0.2

0.35⫾0.05
0.15⫾0.03
0.04⫾0.01

1.10⫾0.10
0.50⫾0.05
0.10⫾0.02

1.85⫾0.15
0.85⫾0.10
0.23⫾0.05

1.35⫾0.20
1.05⫾0.10
0.32⫾0.07⫺1⬍cos ␪⬍⫺0.6⫺0.6⬍cos ␪⬍⫺0.2

0.35⫾0.05
0.15⫾0.03

1.15⫾0.10
0.45⫾0.05

1.65⫾0.10
0.80⫾0.10

1.50⫾0.15
1.20⫾0.10⫺0.2⬍cos ␪⬍0.2

0.06⫾0.01

0.12⫾0.02

0.22⫾0.04

0.31⫾0.06

vor flux ratio of 1:1:1 upon detection, in this figure we scale
limits derived under different assumptions accordingly. For
example, to do a side-by-side comparison of a limit on theflux of ␯ e ⫹ ␯ ␮ ⫹ ␯ ␶ ⫹¯␯ e ⫹¯␯ ␮ ⫹¯␯ ␶ , derived under the assumption of a ratio of 1:1:1, to a limit on just the flux of␯ ␮ ⫹¯␯ ␮ , the latter must be degraded by a factor of three.

FIG. 7. Distribution of ␯ e , ␯ ␮ and ␯ ␶ energies after all selection
criteria have been applied. The relative normalization between thehistograms indicates the relative number of events for each neutrino
flavor that passes all the selection criteria. The initial energy distribution follows an E ⫺2 spectrum. Neutrino absorption inside Earth,
NC scattering and ␶ decay have been taken into account as described in Sec. IV C.

FIG. 8. The limits on the cascade-producing neutrino flux,
summed over the three active flavors, presented in this work and inother experiments, with multiplicative factors applied as indicatedto permit comparison of limits derived with different assumed neutrino fluxes at the detector: Baikal (¯␯ e ) 关38兴 共at the W ⫾ resonance兲;Baikal NT96 ( ␯ ␮ ⫹¯␯ ␮ ⫹ ␯ e ) 关39兴; Frejus ( ␯ ␮ ⫹¯␯ ␮ ) 关40兴; MACRO( ␯ ␮ ⫹¯␯ ␮ ) 关41兴; Baikal NT96⫹NT200 ( ␯ l ⫹¯␯ l ) 关38,42兴;
AMANDA-B10 ( ␯ ␮ ⫹¯␯ ␮ ) 关13兴. Also shown are the predicted horizontal and vertical ␯ e and ␯ ␮ atmospheric fluxes 关32兴.

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共N.B.: We assume that ␯ : ¯␯ ::1:1.兲 Following the Learned andMannheim prescription for presenting limits 关37兴, we show
neutrino energy distributions after applying all the selection
criteria in Fig. 7.
It should be noted that most searches of diffuse fluxes
shown in Fig. 8 are based on the observation of up-goingneutrino-induced muons. Only Baikal and AMANDA havepresented limits from analyses that search for neutrinoinduced cascades and only the AMANDA analysis uses fullcascade event reconstruction.

⫹␯␶⫹¯␯e⫹¯␯␮⫹¯␯␶ is E 2 (d⌽/dE)⬍9.8⫻10⫺6 GeV cm⫺2s⫺1 sr⫺1 assuming a neutrino flavor flux ratio of 1:1:1 at thedetector. The limit on cascades from a diffuse flux of ␯ e⫹¯␯ e is E 2 (d⌽/dE)⬍6.5⫻10⫺6 GeV cm⫺2 s⫺1 sr⫺1 , independent of the assumed neutrino flux ratio. The limits arevalid for neutrino fluxes in the energy range of 5 TeV to 300
TeV.
ACKNOWLEDGMENTS

High-energy neutrino-induced cascades have been
searched for in the data collected by AMANDA-B10 in
1997. Detailed event reconstruction was performed. Using insitu light sources and atmospheric muon catastrophic energy
losses, the sensitivity of the detector to high-energy cascades
has been demonstrated.
No evidence for the existence of a diffuse flux of neutrinos producing cascade signatures has been found. Effective
volumes as a function of energy and zenith angle for all
neutrino flavors have been presented. The effective volumes
allow the calculation of limits for any predicted neutrino flux
model. The limit on cascades from a diffuse flux of ␯ e ⫹ ␯ ␮This research was supported by 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; Swedish Natural Science Research Council;
Swedish Research Council; Swedish Polar Research Secretariat; Knut and Alice Wallenberg Foundation, Sweden; German Ministry for Education and Research; U.S. National Energy Research Scientific Computing Center 共supported by
the Office of Energy Research of the U.S. Department ofEnergy兲; UC-Irvine AENEAS Supercomputer Facility; Deutsche Forschungsgemeinschaft 共DFG兲. D.F.C. acknowledges
the support of the NSF CAREER program and C.P. de los H.
acknowledges support from the EU 4th framework of Training and Mobility of Researchers.

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VIII. CONCLUSIONS

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