Observation of high energy atmospheric neutrinos with the Antarctic muon

and neutrino detector array

J. Ahrens,

E. Andre

X. Bai,

G. Barouch,

S. W. Barwick,

R. C. Bay,

T. Becka,

K.H. Becker,

D. Bertrand,

F. Binon,

A. Biron,

J. Booth,

O. Botner,

A. Bouchta,

O. Bouhali,

M. M. Boyce,

S. Carius,

A. Chen,

D. Chirkin,

J. Conrad,

J. Cooley,

C. G. S. Costa,

D. F. Cowen,

E. Dalberg,

14,†

C. De Clercq,

T. DeYoung,

11,‡

P. Desiati,

J.P. Dewulf,

P. Doksus,

J. Edsjo

P. Ekstro

T. Feser,

J.M. Fre

re,

T. K. Gaisser,

M. Gaug,

4,§

A. Goldschmidt,

A. Hallgren,

F. Halzen,

K. Hanson,

R. Hardtke,

T. Hauschildt,

M. Hellwig,

H. Heukenkamp,

G. C. Hill,

P. O. Hulth,

S. Hundertmark,

J. Jacobsen,

A. Karle,

J. Kim,

B. Koci,

L. Ko

pke,

M. Kowalski,

J. I. Lamoureux,

H. Leich,

M. Leuthold,

P. Lindahl,

I. Liubarsky,

P. Loaiza,

D. M. Lowder,

J. Madsen,

P. Marciniewski,

13,¶

H. S. Matis,

C. P. McParland,

T. C. Miller,

, Y. Minaeva,

P. Mioc

inovic

P. C. Mock,

8,††

R. Morse,

T. Neunho

ffer,

P. Niessen,

4,15

D. R. Nygren,

H. O

gelman,

Ph. Olbrechts,

C. Pe

rez de los Heros,

A. C. Pohl,

R. Porrata,

8,‡‡

P. B. Price,

G. T. Przybylski,

K. Rawlins,

C. Reed,

8,§§

W. Rhode,

M. Ribordy,

S. Richter,

J. Rodrı

guez Martino,

P. Romenesko,

D. Ross,

H.G. Sander,

T. Schmidt,

D. Schneider,

R. Schwarz,

A. Silvestri,

2,4

M. Solarz,

G. M. Spiczak,

C. Spiering,

N. Starinsky,

11,

D. Steele,

P. Steffen,

R. G. Stokstad,

O. Streicher,

P. Sudhoff,

K.H. Sulanke,

I. Taboada,

L. Thollander,

T. Thon,

S. Tilav,

M. Vander Donckt,

C. Walck,

C. Weinheimer,

C. H. Wiebusch,

C. Wiedeman,

R. Wischnewski,

H. Wissing,

K. Woschnagg,

W. Wu,

G. Yodh,

and S. Young

AMANDA Collaboration

Bartol Research Institute, University of Delaware, Newark, Delaware 19716

Fachbereich 8 Physik, BUGH Wuppertal, D42097 Wuppertal, Germany

Universite

Libre de Bruxelles, Science Faculty CP230, Boulevard du Triomphe, B1050 Brussels, Belgium

DESYZeuthen, D15735 Zeuthen, Germany

Department of Technology, Kalmar University, S39182 Kalmar, Sweden

Lawrence Berkeley National Laboratory, Berkeley, California 94720

Department of Physics, University of California, Berkeley, California 94720

Department of Physics and Astronomy, University of California, Irvine, California 92697

Institute of Physics, University of Mainz, Staudinger Weg 7, D55099 Mainz, Germany

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706

Physics Department, University of Wisconsin, River Falls, Wisconsin 54022

Division of High Energy Physics, Uppsala University, S75121 Uppsala, Sweden

Department of Physics, Stockholm University, SCFAB, SE10691 Stockholm, Sweden

Vrije Universiteit Brussel, Dienst ELEM, B1050 Brussel, Belgium

Received 1 February 2002; published 31 July 2002

The Antarctic muon and neutrino detector array

AMANDA

began collecting data with ten strings in 1997.

Results from the first year of operation are presented. Neutrinos coming through the Earth from the Northern

Hemisphere are identified by secondary muons moving upward through the array. Cosmic rays in the atmo

sphere generate a background of downward moving muons, which are about 10

times more abundant than the

upward moving muons. Over 130 days of exposure, we observed a total of about 300 neutrino events. In the

same period, a background of 1.05

cosmic ray muon events was recorded. The observed neutrino flux is

consistent with atmospheric neutrino predictions. Monte Carlo simulations indicate that 90% of these events lie

in the energy range 66 GeV to 3.4 TeV. The observation of atmospheric neutrinos consistent with expectations

establishes AMANDAB10 as a working neutrino telescope.

DOI: 10.1103/PhysRevD.66.012005 PACS number

: 95.85.Ry, 95.55.Vj, 96.40.Tv

Now at CERN, CH1211, Gene

ve 23, Switzerland.

†

Now at Defense Research Establishment

FOA

, S17290 Stockholm, Sweden.

‡

Now at Santa Cruz Institute for Particle Physics, University of California—Santa Cruz, Santa Cruz, CA 95064.

Now at IFAE, 08193 Barcelona, Spain.

Now at MontaVista Software, 1237 E. Arques Ave., Sunnyvale, CA 94085.

Now at The Svedberg Laboratory, S75121 Uppsala, Sweden.

Now at Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723.

††

Now at Optical Networks Research, JDS Uniphase, 100 Willowbrook Rd., Freehold, NJ 077282879.

‡‡

Now at L174, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550.

§§

Now at Dept. of Physics, Massachussetts Institute of Technology, Cambridge, MA.

Now at SNO Institute, Lively, ON, Canada P3Y 1M3.

PHYSICAL REVIEW D

, 012005

2002

05562821/2002/66

/012005

0120051

I. INTRODUCTION

Energetic cosmic ray particles entering the Earth’s atmo

sphere generate a steady flux of secondary particles such as

electrons, muons and neutrinos. The electronic component of

cosmic rays is quickly absorbed. High energy muons pen

etrate the Earth’s surface for several kilometers, while atmo

spheric neutrinos can easily pass the Earth up to very high

energies. Interactions of hadronic particles, similar to the

ones that create the atmospheric neutrino flux, will generate

neutrinos at sites where cosmic rays are generated and where

they interact as they travel through the Universe. The goal of

observing neutrinos of astrophysical origin determines the

design and the size of neutrino telescopes.

The primary channel through which neutrino telescopes

detect neutrinos above energies of a few tens of GeV is by

observing the Cherenkov light from secondary muons pro

duced in

nucleon interactions in or near the telescope. To

ensure that the observed muons are produced by neutrinos,

the Earth is used as a filter and only upward moving muons

are selected. A neutrino telescope consists of an array of

photosensors embedded deeply in a transparent medium. The

tracks of high energy muons—which can travel many hun

dreds of meters, or even kilometers, through water or ice—

can be reconstructed with reasonable precision even with a

coarsely instrumented detector, provided the medium is suf

ficiently transparent. A location deep below the surface

serves to minimize the flux of cosmicray muons.

In this paper we demonstrate the observation of atmo

spheric muon neutrinos with the Antarctic muon and neu

trino detector array

AMANDA

. These neutrinos constitute

a convenient flux of fairly well known strength, angular dis

tribution, and energy spectrum, which can be used to verify

the response of the detector. The paper will focus on the

methods of data analysis and the comparison of observed

data with simulations. After a brief description of the detec

tor, the data and the methods of simulation are introduced in

Sec. III and the general methods of event reconstruction are

described in Sec. IV. Two AMANDA working groups ana

lyzed the data in parallel. The methods and results of both

analyses are described in Secs. V and VI. After a discussion

of systematic uncertainties in Sec. VII we present the final

results and conclusions.

II. THE AMANDA DETECTOR

The AMANDA detector uses the 2.8 km thick ice sheet at

the South Pole as a neutrino target, Cherenkov medium and

cosmic ray flux attenuator. The detector consists of vertical

strings of optical modules

OMs

—photomultiplier tubes

sealed in glass pressure vessels—frozen into the ice at depths

of 1500–2000 m below the surface. Figure 1 shows the cur

rent configuration of the AMANDA detector. The shallow

array, AMANDAA, was deployed at depths of 800 to 1000

m in 1993–1994 in an exploratory phase of the project. Stud

ies of the optical properties of the ice carried out with

AMANDAA showed a high concentration of air bubbles at

these depths, leading to strong scattering of light and making

accurate track reconstruction impossible. Therefore, a deeper

array of ten strings with 302 OMs was deployed in the aus

tral summers of 1995–1996 and 1996–1997 at depths of

1500–2000 m. This detector is referred to as AMANDA

B10, and is shown in the center of Fig. 1. The detector was

augmented by three additional strings in 1997–1998 and six

in 1999–2000, forming the AMANDAII array.

In AMANDA B10, an optical module consists of a single

8 in. Hamamatsu R59122 photomultiplier tube

PMT

housed in a glass pressure vessel. The PMT is optically

coupled to the glass housing by a transparent gel. Each mod

ule is connected to electronics on the surface by a dedicated

electrical cable, which supplies high voltage and carries the

anode signal of the PMT. For each event, the optical module

is read out by a peaksensing ADC and a TDC capable of

registering up to eight separate pulses. The overall precision

of measurement of photon arrival times is approximately

5 ns. Details of deployment, electronics and data acquisition,

calibration, and the measurements of geometry, timing reso

lution, and the optical properties of the ice can be found in

1,2

The optical properties of the polar ice in which

AMANDA is embedded have been studied in detail, using

both light emitters located on the strings and the downgoing

muon flux itself. These studies

have shown that the ice is

not perfectly homogeneous, but rather that it can be divided

into several horizontal layers which were laid down by vary

ing climatological conditions in the past

. Different con

centrations of dust in these layers lead to a modulation of the

FIG. 1. The present AMANDA detector. This paper describes

data taken with the ten inner strings shown in expanded view in the

bottom center.

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

0120052

scattering and absorption lengths of light in the ice, as shown

in Fig. 2. The average absorption length is about 110 m at a

wavelength of 400 nm at the depth of the AMANDAB10

array, and the average effective scattering length is approxi

mately 20 m.

III. DATA AND SIMULATION

The data analyzed in this paper were recorded during the

austral winter of 1997, from April to November. Subtracting

downtime for detector maintenance, removing runs in which

the detector behaved abnormally and correcting for deadtime

in the data acquisition system, the effective livetime was

130.1 days.

Triggering was done via a majority logic system, which

demanded that 16 or more OMs report signals within a slid

ing window of 2

s. When this condition was met, a trigger

veto was imposed and the entire array read out. The raw

trigger rate of the array was on average 75 Hz, producing a

total data set of 1.05

events.

Random noise was observed at a rate of 300 Hz for OMs

on the inner four strings and 1.5 kHz for tubes on the outer

six, the difference being due to different levels of concentra

tion of radioactive potassium in the pressure vessels

details

on noise rates can be found in Ref.

. A typical event has

a duration of 4.5

s, including the muon transit time and the

light diffusion times, so random noise contributed on average

one PMT signal per event.

Almost all of the events recorded were produced by

downgoing muons originating in cosmic ray showers. Trig

gers from atmospheric neutrinos contribute only a few tens

of events per day, a rate small compared to the event rate

from cosmic ray muons, as shown in Fig. 3. The main task of

AMANDA data analysis is to separate these neutrino events

from the background of cosmicray muons. Monte Carlo

simulations of the detector response to muons pro

duced by neutrinos or by cosmic rays were undertaken to

develop techniques of background rejection.

Downgoing muons were generated by atmospheric

shower simulations of isotropic protons with

BASIEV

protons and heavier nuclei with

CORSIKA using the QGSJET

generator

7,8

, and tracked to the detector with the muon

propagation code

MUDEDX

9,10

. Two other muon propaga

tion codes were used to check for systematic differences:

PROPMU

with a 30% lower rate and

MMC

with a

slightly higher rate. A total of 0.9

events were simu

lated. Most characteristics of the events generated with

BASIEV

were found to be similar to the more accurate

CORSIKAbased simulation. For the latter, the primary cosmic

ray flux as described by WiebelSooth and Biermann

was used. The curvature of the Earth has been implemented

CORSIKA to correctly describe the muon flux at large ze

nith angles. The event rate based on this Monte Carlo was 75

Hz and compares reasonably well with the observed rate of

100 Hz

after deadtime correction

. The detector response to

muons was modeled by calculating the photon fields pro

duced by continuous and stochastic muonic energy losses

, and simulating the response of the hardware to these

photons

15,16

. Upgoing muons were generated by a propa

gation of atmospheric neutrinos, which were tracked through

the Earth and allowed to interact in the ice in or around the

detector or in the bedrock below

17,18

. Muons that were

generated in the bedrock were propagated using

PROPMU

until they reached the rockice boundary at the depth of 2800

m. The muons were then propagated through the ice in the

same way as those from cosmic ray showers. The atmo

spheric neutrino flux was taken from Lipari

The Cherenkov photon propagation through the ice was

modeled to create multidimensional tables of density and

FIG. 2. Variation of the optical properties with depth. The effec

tive scattering coefficient at a wavelength of 532 nm is shown as a

function of depth. The

axis is pointing upwards and denotes the

vertical distance from the origin of the detector coordinate system

located at a depth of 1730 m. The shaded areas on the side indicate

layers of constant scattering coefficient as used in the Monte Carlo

simulation.

FIG. 3. The zenith angle distribution of simulated AMANDA

triggers per 130.1 days of lifetime. The solid line represents triggers

from downgoing cosmic ray muons generated by

CORSIKA. The

dashed line shows triggers produced by atmospheric neutrinos.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

0120053

arrival time probability distributions of the photon flux.

These photon fields were calculated for pure muon tracks

and for cascades of charged particles. A real muon track was

modeled as a superposition of the photon fields of a pure

muon track and the stochastic energy losses based on cas

cades. The photon fields were calculated out to 400 m from

the emission point, taking into account the orientation of the

OM with respect to the muon or cascade. In the detector

simulation, the ice was modeled as 16 discrete layers, as

indicated by the shaded areas in Fig. 2. The spectral proper

ties of the photomultiplier sensitivity, the glass, the gel, and,

most importantly, the ice itself were included in the simula

tion of the photon propagation. The probability of photon

detection depends on the Fresnel reflectance at all interfaces,

transmittances of various parts, and quantum and collection

efficiencies of the PMT. The relevant physical parameters

have been measured in the laboratory, so that the spectral

sensitivity of the OM could be evaluated. Two types of OMs,

differing in the type of pressure vessel, were used in the

construction of AMANDAB10. The inner four strings

AMANDAB4

use Billings housings while the outer six

strings use Benthos housings.

Benthos Inc. and Billings In

dustries are the manufacturers of the glass pressure vessels.

Benthos and Billings are registered trademarks of the respec

tive companies.

The two types of housing have different

optical properties. The Benthos OMs have an effective quan

tum efficiency of 21% at a wavelength of 395 nm for plane

wave photons incident normal to the PMT photocathode.

Ninety percent of the detected photons are in the spectral

range of 345–560 nm.

An additional sensitivity effect arises from the ice sur

rounding the OMs. The deployment of OMs requires melting

and refreezing of columns of ice, called ‘‘hole ice’’ hereafter.

This cycle results in the formation of bubbles in the vicinity

of the modules, which increase scattering and affects the

sensitivity of the optical modules in ways that are not under

stood in detail. Since the total volume of hole ice is small

compared to bulk ice in the detector

columns of 60 cm di

ameter, compared to 30 m spacing between strings

, its effect

on optical properties can be treated as a correction to the OM

angular sensitivity. The increased scattering of photons in the

hole ice has been simulated and compared to data taken with

laser measurements

in situ

to assess the magnitude of this

effect. This comparison provides an OM sensitivity correc

tion that reduces the relative efficiency in the forward direc

tion, but enhances it in the sideways and backward direc

tions. The sensitivity in the backward hemisphere

(90° –180°) relative to the sensitivity integrated over all

angles (0° –180°) of the optical sensor increases from 20%

to 27%, due to this correction, while the average relative

sensitivity in the forward direction (0° –90°) drops from

80% to 73%. In other words, an OM becomes a somewhat

more isotropic sensor.

The effective angular sensitivity of the OMs was also as

sessed using the flux of downgoing atmospheric muons as a

test beam illuminating both the 295 downward facing OMs

and the 7 upward facing OMs. We assumed that the response

of the upward facing OMs to light from downward muons is

equivalent to the response of the downward facing OMs to

light from upward moving muons. Based on this assumption

we derived a modified angular response function

later re

ferred to as

ANGSENS

, which resulted in a effective reduc

tion of the absolute OM sensitivity in forward direction. In

this model the effective relative sensitivity is 67% in the

forward hemisphere, and 33% in the backward hemisphere.

This correction will be used to estimate the effect of system

atic uncertainties in the angular response on the final neu

trino analysis.

The simulation of the hardware response included the

modeling of gains and thresholds and random noise at the

levels measured for each OM. The transit times of the cables

and the shapes of the photomultiplier pulses, ranging from

170 to 360 ns full width at half maximum

FWHM

, were

included in the trigger simulation. Multiphoton pulses were

simulated as superimposed single photoelectron waveforms.

In all, some 8

seconds of cosmic rays were simulated,

corresponding to 7% of the events contained in the 1997 data

set.

IV. EVENT RECONSTRUCTION

The reconstruction of muon events in AMANDA is done

offline, in several stages. First, the data are ‘‘cleaned’’ by

removing unstable PMTs and spurious PMT signals

‘‘hits’’

due to electronic or PMT noise. The cleaned events

are then passed through a fast filtering algorithm, which re

duces the background of downgoing muons by one order of

magnitude. This reduction allows the application of more

sophisticated reconstruction algorithms to the remaining data

set.

Because of the complexity of the task, and in order to

increase the robustness of the results, two separate analyses

of the 1997 data set were undertaken. Both proceeded along

the general lines described above, but differ in the details of

implementation. The preliminary stages, which are very

similar in both analyses, are described here. The particulars

of each analysis will be described in Secs. V and VI. A more

detailed description of the reconstruction procedure will be

published elsewhere

A. Cleaning and filtering

The first step in reconstructing events is to clean and cali

brate the data recorded by the detector. Unstable channels

OMs

are identified and removed on a runtorun basis. On

average, 260 of the 302 OMs deployed are used in the analy

ses. The recorded times of the hits are corrected for delays in

the cables leading from the OMs to the surface electronics

and for the amplitudedependent time required for a pulse to

cross the discriminator threshold. Hits are removed from the

event if they are identified as being due to instrumental

noise, either by their low amplitudes or short pulse lengths,

or because they are isolated in space by more than 80 m and

time by more than 500 ns from the other hits recorded in the

event. Pulses with short duration, measured as the time over

threshold

TOT

, are often related to electronic crosstalk in

the signal cables or the surface electronics. In analysis II,

TOT cuts are applied to individual channels beyond the stan

dard cleaning common to both analyses

see Sec. VI

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

0120054

Following the cleaning and the calibration, a ‘‘line fit’’ is

calculated for each event. This fit is a simple

minimiza

tion of the apparent photon flux direction, for which an ana

lytic solution can be calculated quickly

see also Fig. 14

top

demonstrating the effect for analysis II

, while the horizontal

components (

COG

and

COG

) show an enhancement of hits

towards the outer strings. These strings are read out via

twisted pair cables, as opposed to the coaxial cables used on

the inner strings. The twisted pair cables were found to be

more susceptible to crosstalk signals. Note that variations in

the optical parameters of the ice due to past climatological

episodes also produce some vertical structure.

We developed additional COG cuts on the topology of the

events in order to remove these backgrounds. These cuts,

which depend on the reconstructed zenith angle, use the

track lengths

dir

and the normalized smallest eigenvalues of

the tensor of inertia (

(

FIG. 6. Illustration of the smoothness parameter, which com

pares the observed distribution of hits to that predicted for a muon

emitting Cherenkov light. In the simplest formulation, shown here,

the prediction is given as a straight line. A large deviation from a

straight line

0. 68

is found for the event on the right in Fig. 5. The

high quality tracklike event on the left in Fig. 5 displays a small

deviation

0.09

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

0120057

Figure 7 shows the different components of the center of

gravity of the hits and the reconstructed zenith angle before

and after application of the COG cuts, and the Monte Carlo

prediction for fake upward events stemming from misrecon

structed downgoing muons. The cuts remove most of the

unsimulated background—in particular that far from the

horizon—and bring experiment and simulation into much

better agreement.

In order to verify the signal passing rates, these cuts and

those from the previous levels were applied to a subsample

of unfiltered

i.e., downgoing

events but with the zenith

angle dependence of the cuts reversed, thus using the abun

dant cosmic ray muons as standins for upgoing muons.

In all, these three levels of filtering reduced the data set by

a factor of approximately 10

see Table II

B. Multiphotoelectron likelihood and hit likelihood

Before the final cut optimization the last, most elaborate

reconstruction was applied, combining the likelihoods for the

arrival time of the first of muliple photons in a PMT with the

likelihoods for PMTs to have been hit or have not been hit.

The probability densities

(

res

(

)

’

(

)

ori

(

)

see Eq.

Sec. IV B

describe only the arrival times of single photons.

Density functions for the multiphotoelectron case have to

include the effect of repeatedly sampling the distribution of

photon arrival times. For several detected photons, the first

of them is usually less scattered than the average photon

which defines the single photoelectron case

. Therefore the

leading edge of a PMT pulse composed of multiple photo

electrons

MPE

will be systematically shifted to earlier

times compared to a single photoelectron. The

MPE likeli

hood

time

MPE

uses the recorded amplitude information to

model this shift.

In the reconstructions mentioned so far, the timing infor

mation from hit PMTs was used. However, a PMT which

was

not

hit also delivers information. The

hit likelihood

hit

does not depend on the arrival times but represents the prob

ability that the track produced the observed hit pattern. It is

constructed from the probability densities

hit

(

’

(

)

ori

(

)

) that

a given PMT

was hit if it was in fact hit, and the probabili

ties

hit

(

’

(

)

ori

(

)

that a given PMT

was not hit if it

was not hit:

hit

)

hit

’

(

)

ori

(

)

hit

’

(

)

ori

(

)

where the first product runs over all hit PMTs and the second

over all nonhit PMTs.

The likelihood combining these two probabilities is

FIG. 7. Characteristic distributions of the cen

ter of gravity

COG

of events. The figures on the

left show the distribution of the depth

COG

ver

sus the reconstructed zenith angle. The figures on

the right show the horizontal location of events in

the

COG

plane of events with 0 m

COG

50 m. The positions of the strings are marked

by stars. Top: Experimental data before applica

tion of the COG cuts. Middle: Experimental data

after application of the COG cuts. Bottom: Ex

pectation from the BG simulation after cuts.

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

0120058

time

MPE

hit

A cut on the reconstructed zenith angle obtained from

fitting with

leaves less than 10

events in the data set,

defined as level 4 in Fig. 8.

C. Final separation of the neutrino sample

For the final stage of filtering, a method

CUTEVAL

was

developed to select and optimize the cuts taking into account

correlations between the cut parameters. A detailed descrip

tion of this method can be found in

. The principle of

CUTEVAL

is to numerically optimize the ratio of signal to

background by variation of the selection of cut parameters,

as well as the actual cut values. Parameters are used only if

they improve the efficiency of separation over optimized cuts

on all other already included parameters. A first optimization

was based purely on Monte Carlo simulations, with simu

lated atmospheric neutrinos for signal and simulated down

going muons forming the background. This optimization

yielded four such independent parameters. Two other optimi

zations involved experimental data. In both cases, experi

mental data have been defined as the background sample. In

one case, the signal was represented by atmospheric neutrino

Monte Carlo simulations, in the other by experimental data

subjected to zenith angle inverted cuts

i.e., to downward

events passing the quality cuts, but being ‘‘good’’ events

with respect to the upper hemisphere instead—like neutrino

candidates—with respect to the lower hemisphere

. These

latter optimizations yielded two additional parameters, which

rejected a small contribution of residual unsimulated back

grounds: coincident muons from simultaneous independent

air showers and events accompanied by instrumental artifacts

such as crosstalk. After application of these two cuts to

simulated and experimental data, the distributions of observ

ables agree to a satisfactory precision.

Once the minimal set of parameters is found, the optimal

cut values can be represented as a function of the number of

background events

passing the cuts. The result is a path

through the cut parameter space which yields the best signal

efficiency for any desired purity of the signal, characterized

. Using this representation, one can calculate the

number of events passing the cuts as a function of the fitted

for signal and for background Monte Carlo program.

Figure 8

top

shows this dependence for simulations as well

as for experimental data, with

varying from trigger level

to a level that leaves only a few events in the data set. One

observes that the actual background expectation falls roughly

linearly as the fitted

is reduced. Below values of a few

hundred events the signal is expected to dominate the event

sample. The experimental curve follows the expectation from

the sum of background and signal Monte Carlo program. For

large

, the observed event rate follows the background

expectation. At smaller

, the experimental shape turns

over into the signal expectation and follows it nicely down to

the sample of events with highest quality

the smallest values

. For a moderate background contamination of

10, one gets a total of 223 neutrino candidates. The param

eters and cut values as obtained by the

CUTEVAL procedure

are summarized in Table I.

Figure 8

bottom

translates the background parameter

into an event quality parameter

, defined as

[

ln(

)

ln(1.05

). The plot shows the ratios

FIG. 8. The fitted background parameter

. Top: Number of

events versus

. Smaller values of

correspond to harder

cuts. Below

1500 the

CUTEVAL

parametrization was used to

calculate the cut values corresponding to

. For larger values of

the data points correspond to the cuts from the filter levels:

Level 4

see Sec. V B

, level 3, level 2, level 1, and trigger level

Table II

. Bottom: Ratios of events passing in the experimental

data compared to various Monte Carlo expectations for signal and

background as a function of event quality. The dashed line indicates

the final cuts.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

0120059

of events from the upper figure as a function of

. At higher

qualities (

17), the ratio of observed events to the atmo

spheric neutrino simulation flattens out with a further varia

tion of only 30%. The value at

17 is approximately 0.6

for the standard Monte Carlo program

chosen in Fig. 8, top

and approximately unity for the

ANGSENS Monte Carlo pro

gram

chosen in Fig. 8, bottom

Table II lists the cut efficiencies for the atmospheric neu

trino simulation

with and without the implementation of the

angular sensitivity fitted model

ANGSENS

of the OMs—see

Secs. III and VII

, the background simulation of atmospheric

muons from air showers

without

ANGSENS

and the experi

mental data. Again, the experimental numbers agree well

with the background simulation up to the first two filter lev

els. Later, the Monte Carlo program underestimates the ex

perimental passing rates slightly. The last row shows the ex

pected numbers of events for the last stage of filtering. If, in

addition, the effect of neutrino oscillations

see Sec. VII

included, the atmospheric neutrino simulation including the

ANGSENS

model predicts 224 events, in closest agreement

with the experiment. However, the 5% effect due to oscilla

tions is smaller than our systematic uncertainty

see Sec.

VII

D. Characteristics of the neutrino candidates

1. Time distribution

Figure 9 shows the cumulative number of neutrino events

as well as the cumulative number of event triggers plotted

versus the day number in 1997. One can observe that the

neutrino events follow the number of triggers, albeit with a

small deficit during the Antarctic winter. This deficit is con

sistent with statistical fluctuations.

Actually, seasonal varia

tions slightly

crease the downward muon rate during the

Antarctic winter

and should result in a 10% deficit of

triggers with respect to upward neutrino events.

TABLE I. Final quality parameters and cuts obtained from the cut evaluation procedure. The ‘‘direct’’

time interval for variables

dir

, and

dir

15 ns,

75 ns

. The first four rows show cut parameters

obtained by all

Monte Carlo and experimental

searches; the last two rows show two additional

weaker

cuts, which were found to remove unsimulated backgrounds.

Parameter Cut Explanation

0.28 See Sec. IV C 4

hit

mpe

90°)

0.01 Tightens the requirement on the smoothness for

tracks

close to the horizon where background is high

(

dir

750 m Lever arm of the track times the number of

supporting points

log(

down

)

7.7 Ratio of the likelihoods of the best

upgoing and best downgoing hypotheses

(mpe,lf)

35° Space angle between the results from the

multiphoton

likelihood reconstruction and the line fit. This cut

effectively removes crosstalk features.

(

dir

)

(

dir

hit

)

0.55 Parameter combining the two smoothness

definitions

here calculated using only direct hits

This cut effectively removes coincident muon

events from independent air showers.

TABLE II. The cut efficiencies for the atmospheric neutrino Monte Carlo

prediction, the atmo

spheric muon background Monte Carlo prediction, and the experimental data for 130 days of detector

lifetime. Efficiencies are given for filter levels L1 to L4. L4 is the final selection. All errors are purely

statistical. The final background prediction of 7 events has been normalized at trigger level.

Filter level Atm.

Atm.

MC Atm.

MC Experimental

ANGSENS

Background

data

Events at trigger level 8978 5759 9.03

1.05

Efficiency at level 1 0.34 0.37 0.4

0.5

Efficiency at level 2 0.15 0.15 0.4

0.4

Efficiency at level 3 0.7

0.7

0.1

Efficiency after final cuts 0.4

0.4

0.6

0.2

No. of events 362

4 237

5 223

passing final cuts normalized

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200510

2. Zenith angle distribution

Figure 10 shows the zenith angle distribution of the 223

neutrino candidates compared to the Monte Carlo prediction

for atmospheric neutrinos

and the few remaining events

predicted by background simulations. Note that the Monte

Carlo prediction is normalized to experiment.

The total

number of events is 362 for the atmospheric neutrino simu

lation and 223 for experiment, i.e., there is a deficit of 39

percent in the absolute number of events.

There is good

agreement between the prediction and the experiment in the

shape of the angular distribution.

3. Characteristic distributions and visual inspection

Four methods were used to evaluate the effectiveness of

the analysis and the level of residual backgrounds:

cuts

unbiased variables

low level distributions

and

visual inspection

The

test

evaluates the

final cuts one by one

and yields an estimate of the background contamination in

the final sample. One applies all but one of the final cuts

the

one in the selected variable

, and plots the data in this vari

able. In the signal region of this variable

defined by the later

applied cut

shapes of experiment and signal Monte Carlo

program should agree. In the background region, the experi

mental data should approach the expected background shape.

Figure 11 shows four of these distributions. The applied cut

is shown by a dotted line. All four cuts satisfy the test: the

shape of the distributions agree reasonably well on both sides

of the applied cuts. Two

1 distribution from analysis II

are shown in Fig. 19.

An obvious test is the investigation of distributions of

unbiased variables

i.e., variables to which no cuts have

been applied

in the final neutrino sample. Here, the experi

mental distributions follow the Monte Carlo signal expecta

tions nicely. Some deviations are observed, especially in the

number of OMs hit and the velocity

obtained from the

line fit

see Sec. IV A

. However, as can be seen from Fig.

20, part of these disagreements disappear if the standard at

mospheric neutrino MC program is replaced by the

ANGSENS

MC version.

In order to account for possible pathological

low level

features in the data sample

especially crosstalk

,we

vestigated basic pulse amplitude and pulse width

TOT

dis

tributions and

refitted all events after the crosstalk hit

cleaning procedure applied in analysis II

which is tighter

than the standard crosstalk cleaning introduced in Sec.

IV A

. Both these distributions and that for the recalculated

zenith angles show no significant deviation from the previ

ous ones. No crosstalk features are found in the resulting

neutrino sample.

Finally, a

visual inspection

of the full neutrino sample

was performed, by visually displaying each event like in Fig.

4. The visual inspection gives consistent results with the

other methods of background estimation and yields an upper

limit on the background contamination of muons from ran

dom coincident air showers

see below

E. Background estimation

The results of four independent methods of background

estimation are summarized in Table III.

First, the background Monte Carlo program itself gives an

estimate. It yields 7 events if rates are normalized to the

trigger level

see Table II

. Because the passing rates differ

slightly between the experiment

higher

and the background

Monte Carlo program

lower

, we made the conservative

choice to renormalize the background Monte Carlo program

to the level 3 experimental passing rate. This gives an esti

mate of about 16 background events in our final sample.

From the

1 distributions we obtained an alternative

approximation of the residual background. We renormalized

both signal and background MC events in the background

region to fit the number of experimental events in the back

ground region. The number of renormalized background

FIG. 9. The integrated exposure of the AMANDA detector in

1997. The figure shows the cumulative number of triggers

upper

curve

and the number of observed neutrino events

lower curve

versus the day number. The intervals with zero gradient correspond

to periods where the detector was not operating stably; data from

these periods were excluded from the analysis.

FIG. 10. Zenith angle distribution of the experimental data com

pared to simulated atmospheric neutrinos and a simulated back

ground of downgoing muons produced by cosmic rays. In this fig

ure the Monte Carlo prediction is normalized to the experimental

data. The error bars report only statistical errors.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

01200511

MC events in the signal region is then a background esti

mate. This estimate was performed

times

once for each

1 distribution

. The average over all

estimations yields

14 background events. Note that this averaging procedure is

reasonable only for the case of independent cuts. With the

method by which we have chosen the cut parameters, this

condition is satisfied to first approximation.

We have found that crosstalk hits are related to the char

acteristic triplepeak structure in the distribution of the ver

tical component of the center of gravity of hits (

COG

) which

has been discussed in Sec. V A—see Fig. 7 and also Fig. 14

top

. Since there are remaining cross talk hits which have

survived the standard cleaning

see Sec. IV A

, this distribu

tion was studied in detail. As shown in Fig. 12, the final

experimental sample of neutrino candidates shows no statis

tically significant excess with respect to the atmospheric neu

trino Monte Carlo prediction in the regions of the character

istic peaks. Therefore, an upper limit on this special class of

background was derived and yields

35 events.

The visual inspection of the neutrino sample yields 13

events. Seven of them show the signature of coincident

muons from independent air showers; i.e., two well separated

spatial concentrations of hits, each with a downward time

flow but with the lower group appearing earlier than the up

per one. Taking into account the scanning efficiencies which

were determined by scanning signal and background Monte

Carlo events, an upper limit of 23 events is obtained from

visual inspection.

Combining the results from the above methods, the ex

pected background is estimated to amount to 4 to 10% of the

223 experimental events.

FIG. 11. Two distributions of variables used as cut parameters in

the last filter level

see Table I for an explanation of the variables

In both cases, all final cuts with the exception of the variable plotted

have been applied. The cuts on the displayed parameters are indi

cated by the dashed vertical lines. Arrows indicate the accepted

parameter space.

FIG. 12. Distributions of

COG

for the experiment and atmo

spheric neutrino signal Monte Carlo program

MC standard

and

bulk ice

denote two different ice models. The first includes vertical

ice layers in accordance with Fig. 2; the second uses homogeneous

ice.

TABLE III. Various estimates of the background remaining in

the experimental data sample of 223 neutrino candidates.

BG estimation method Estimation

BG MC 16

1 cuts 14

COG

distributions

Visual inspection

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200512

VI. ANALYSIS II

The second analysis follows a different approach; instead

of optimizing cuts to reject misreconstructed cosmic ray

muons, this analysis concentrates on improving the recon

struction algorithm with respect to background rejection. The

large downgoing muon flux implies that even a small frac

tion of downgoing muons misreconstructed as upgoing will

produce a very large background rate. Equivalently, for each

apparently upgoing event, there were many more downgoing

muons passing the detector than there were upgoing muons;

even though any single downgoing muon had only a small

probability of faking an upgoing event, the total probability

that the event was a fake is quite high.

A. Bayesian reconstruction

This analysis of the problem motivates a Bayesian ap

proach

to event reconstruction. Bayes’ theorem in prob

ability theory states that for two assertions

and

where

(

) is the probability of assertion

given that

is true. Identifying

with a particular muon track hypothesis

and

with the data recorded for an event in the detector,

we have

data

time

data

where we have dropped a normalization factor

(data)

which is a constant for the observed event. The function

time

is the regular likelihood function of Eq.

, and

(

)

is the socalled prior function, the probability of a muon

(

) passing through the detector.

For this analysis, we have used a simple onedimensional

prior function, containing the zenith angle information at

trigger level in Fig. 3. By accounting in the reconstruction

for the fact that the flux of downgoing muons from cosmic

rays is many orders of magnitude larger than that of upgoing

neutrinoinduced muons, the number of downgoing muons

that are misreconstructed as upgoing is greatly reduced. It

should be noted that the objections that are often raised with

respect to the use of Bayesian statistics in physics are not

relevant to this problem: the prior function is well defined

and normalized and independently known to relatively good

precision, consisting only of the fluxes of cosmic ray muons

and atmospheric muon neutrinos.

B. Removal of instrumental artifacts

The Bayesian reconstruction algorithm is highly efficient

at rejecting downgoing muon events. Of 2.6

events

passing the fast filter, only 5.8

are reconstructed as up

going. By contrast, the standard maximum likelihood recon

struction produces about 2.4

false upgoing reconstruc

tions. However, less than a thousand neutrino events are

predicted by Monte Carlo program, so it is clear that a sig

nificant number of misreconstructions remain.

Detailed inspection of the 5.8

events reveals that the

vast majority is produced by crosstalk overlaid on triggers

from downgoing muons emitting bright stochastic light near

the detector. This crosstalk confuses the reconstruction al

gorithm, producing apparently upgoing tracks. Because

crosstalk is not included in the detector simulation, the char

acteristics of the fakes are not predicted well by the simula

tion, and the rate of misreconstruction is much higher than

predicted.

The crosstalk is removed by additional hit cleaning rou

tines developed by examination of this crosstalk enriched

data set. For example, crosstalk in many channels can be

identified in scatter plots of pulse width vs amplitude, as

shown in Fig. 13. The pulse width is measured as time over

threshold

TOT

. Real hits form the distribution shown on

the left. High amplitude pulses should have large pulse

width. This is not the case for crosstalk induced pulses. In

channels with high levels of crosstalk, an additional vertical

FIG. 13. Pulse amplitude vs duration for modules on the outer

strings. Normal hits lie in the distribution shown in the upper figure.

High amplitude pulses of more than a few photoelectrons are valid

only if the pulse width is also large. Crosstalk induced pulses of

high amplitude are characterized by small time over threshold

TOT

. The cutoff seen at high amplitude is due to saturation of the

amplitude readout electronics.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

01200513

band is found at high amplitudes but short pulse widths, as

seen in the lower figure.

Other hit cleaning algorithms use the time correlation and

amplitude relationship between real and crosstalk pulses and

a map of channels susceptible to crosstalk and the channels

to which they are coupled. An additional instrumental effect,

believed to be caused by fluctuating high voltage levels, pro

duces triggers with signals from most OMs on the outer

strings but none on the inner four strings; some 500 of these

bogus triggers were also removed from the data set. The

5.8

upgoing events were again reconstructed after the

additional hit cleaning was applied. Only 4.9

8.4%

the events remained upgoing, compared to an expectation

from Monte Carlo program of 1855 atmospheric muon

events

37.8% of the total before the additional cleaning

and 555 atmospheric neutrino events. Figure 14

top

shows

that while there has been a significant reduction in the instru

mental backgrounds, an unsimulated structure still remains

in the centerofgravity

COG

distribution for these remain

ing data events. The application of additional quality criteria

brings this distribution in agreement, as shown in Fig. 14

bottom

C. Quality cuts

The improvements in the reliability of the reconstruction

algorithm described above obviated the need for large num

bers of cut parameters or for careful optimization of the cuts.

Because the signaltonoise ratio of the upwardreconstructed

data is quite high to begin with, we have the possibility of

comparing the behavior of real and simulated data over a

wide range of cut strengths to verify that the data agree with

the predictions for upgoing neutrinoinduced muons, not

only in number but also in their characteristics. Using the cut

parameters described in Sec. IV C

with the likelihood re

placed by the Bayesian posterior probability

and a require

ment that events fitted as relatively horizontal by the line fit

filtering algorithm not be reconstructed as steeply upgoing

by the full reconstruction

a requirement that suppresses re

sidual crosstalk misreconstructions

, an index of event qual

ity was formed.

To do so, we rescale the six quality parameters described

above by the cumulative distributions of the simulated atmo

spheric neutrino signal, and consider the sixdimensional cut

space formed by the rescaled parameters. A point in this

space corresponds to fixed values of the quality parameters,

and events can be assigned to locations based on their track

length, sphericity, and so forth.

It is difficult to compare the distributions of data and

simulated up and downgoing muons directly because of the

high dimensionality of the space. We therefore project the

space down to a single— ‘‘quality’’ — dimension by divid

ing it into concentric rectangular shells, as illustrated in Fig.

15. The vertex of each shell lies on a line from the origin

through a reference set of cuts which are believed to isolate a

fairly pure set of neutrino events. Events in the full cut space

are assigned an overall quality value, based on the shell in

which they lie.

FIG. 14. Top: Event center of gravity distribution after recon

struction with special crosstalk cleaning algorithms applied to the

events. Unsimulated background remains. Bottom: The data agree

with the neutrino signal after application of additional quality cuts.

FIG. 15. Definition of event quality. Events are plotted in

dimensional cut space

two dimensions are shown here for clar

ity

. A line is drawn from the origin

no cuts

through a selected set

of cuts, and the space is divided into rectangular shells of equal

width. Events are assigned a quality

according to the shell in

which they are found.

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200514

With this formulation we can compare the characteristics

of the data to simulated neutrino and cosmicray muon

events. Figure 16 compares the number of events passing

various levels of cuts; i.e., the integral number of events

above a given quality. At low qualities,

3, the data set is

dominated by misreconstructed downgoing muons, data as

well as the simulated background exceed the predicted neu

trino signal. At higher qualities, the passing rates of data

closely track the simulated neutrino events, and the predicted

background contamination is very low.

We can investigate the agreement between data and

Monte Carlo simulations more systematically by comparing

the differential number of events

within

individual shells,

rather than the total number of events passing various levels

of cuts. This is done in Fig. 17, where the ratios of the

number of events observed to those predicted from the com

bined signal and background simulations are shown. One can

see that at low quality levels there is an excess in the number

of misreconstructed events observed. This is mainly due to

remaining crosstalk. There is also an excess, though statis

tically less significant, at very high quality levels, which is

believed to be caused by slight inaccuracies in the descrip

tion of the optical parameters of the ice. Nevertheless, over

the bulk of the range there is close agreement between the

data and the simulation, apart from an overall normalization

factor of 0.58. The absolute agreement is consistent with the

systematic uncertainties. It should be emphasized that the

quality parameter is a convolution of all six quality param

eters, and so the flat line in Fig. 17 demonstrates agreement

in the correlations between cut parameters.

D. Background estimation and signal description

If we reduce the 4917 upwardreconstructed events by

requiring a quality of at least 7 on the scale of Fig. 16, we

obtain a set of 204 neutrino candidates. The background con

tamination, which is due to misreconstructed downgoing

muons, was estimated in three ways. The first way is to

simulate the downgoing muon flux, bearing in mind that we

are looking at a very low tail (10

) of the total muon dis

tribution. The second way is to renormalize the signal simu

lation by the factor of 0.58 obtained from Fig. 17 and sub

tract the predicted events from the observed data set

accepting the excess at extremely high qualities, however,

as signal

. The third way, a cross check on the first two

methods, is to examine the data looking for fakes due to

unsimulated effects such as crosstalk, independent coinci

dent downgoing muons, and so forth. All three methods yield

estimates of 5–10 % contamination.

The zenith angle distribution for the 204 events is shown

in Fig. 18, and compared to that for the simulation of atmo

spheric neutrinos. In the figure the Monte Carlo events are

normalized to the number of observed events to facilitate

comparison of the shapes of the distributions. The agreement

in absolute number is consistent with the systematic uncer

tainties in the absolute sensitivity and the flux of high energy

atmospheric neutrinos. The shape of the distribution of data

is statistically consistent with the prediction from atmo

spheric neutrinos. Figure 14

bottom

shows the distribution

of the

COG

parameter for the 204 events. The level 7 quality

cuts have removed the remainder of the instrumental events

left after the Bayesian reconstruction with the improved

crosstalk cleaning algorithm, bringing the data events in line

with the atmospheric neutrino expectations. The efficiencies

corresponding to the three steps of the data analysis:

events reconstructed upward,

events reconstructed up

ward with crosstalk cleaning, and

with additional level 7

quality cuts are summarized in Table IV.

Figure 19

top

shows the smoothness distribution for

events that have passed the quality level 7 cuts for the five

observables except smoothness. The vertical dashed line at

smoothness

;

0.29 shows the value of the level 7 smooth

FIG. 16. Numbers of events above a certain quality level, for

downgoing muon Monte Carlo simulations, atmospheric neutrino

Monte Carlo simulations, and experimental data.

FIG. 17. Ratio of data to Monte Carlo simulations

cosmic ray

muons plus atmospheric neutrinos

. Unlike Fig. 16, the plot is

differential—the ratio at a particular quality does not include events

at higher or lower qualities.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

01200515

ness cut. This cut removes the tail of fake events leaving a

good agreement between remaining data and the Monte

Carlo expectation. Figure 19

bottom

shows the same plot

for the direct length variable. Again, a clear tail of fake

events is removed by requiring a direct length of greater than

70 m.

VII. SYSTEMATIC UNCERTAINTIES

As a novel instrument, AMANDA poses a unique chal

lenge of calibration. There are no known natural sources of

high energy neutrinos, apart from atmospheric neutrinos,

whose observation could be used to measure the detector’s

response. Understanding the behavior of the detector is thus

a difficult task, dependent partly on laboratory measurements

of the individual components, partly on observations of arti

ficial light sources embedded in the ice, and partly on obser

vations of downgoing muons. Even with these measure

ments, uncertainties in various properties that systematically

affect the response of the detector persist, which prevent us

at this time from making a precise measurement of the atmo

spheric neutrino flux. The primary sources of systematic un

certainties, and their approximate effects on the number of

upgoing atmospheric neutrinos in the final data sample, as

TABLE IV. Event numbers for experimental data and Monte Carlo simulations for four major stages in

the analysis. The errors quoted are statistical only.

Monte Carlo Monte Carlo Data

downgoing

atmospheric

Events triggered 8.8

8978 1.05

Efficiency: Reconstructed upgoing 0.55

0.55

Efficiency: Reconstructed upgoing (2.1

0.08)

(6.2

0.06)

4.7

with crosstalk cleaning

Efficiency: Final cuts (

7) (1.9

0.6)

(3.1

0.03)

1.9

No. of events: Quality

717

5 279

3 204

FIG. 18. The zenith angle distribution of upward reconstructed

events. The size of the hatched boxes indicates the statistical preci

sion of the atmospheric neutrino simulation. The Monte Carlo pre

diction is normalized to the data.

FIG. 19. Smoothness and direct length variables where quality

level 7 cuts have been applied in all but the displayed variable (

1 cuts; see also Sec. V D 3, Fig. 11

. The vertical dashed lines

with the arrow indicate the region of acceptance in the displayed

variable. In each case, a clear tail of fake events is removed by

application of the cut, leaving good agreement in shape between the

remaining events and the Monte Carlo expectation.

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200516

determined by variation of the simulations, are listed below.

As discusssed in Secs. II and III, AMANDA is embedded

in a natural medium, which is the result of millennia of cli

matological history, that has left its mark in the form of

layers of particulate matter affecting the optical properties of

the ice. Furthermore, the deployment of optical modules re

quires the melting and refreezing of columns of the ice. This

cycle results in the formation of bubbles in the vicinity of the

modules, which increase scattering and affect the sensitivity

of the optical modules in ways that are not yet fully under

stood. The effects of this local hole ice are difficult to sepa

rate from the intrinsic sensitivity of the OMs. The uncertain

ties in the neutrino rate are approximately 15% from the bulk

ice layer modeling in the Monte Carlo simulation, and as

much as 50% from the combined effects of the properties of

the refrozen hole ice close to the OMs, and the intrinsic OM

sensitivity, and angular response.

Figure 20 shows two variables that are sensitive to the

absolute OM sensitivity: the number of OMs hit and the

velocity of the line fit. The systematic effects of varying OM

sensitivity on the hit multiplicity for analysis I are shown on

the top. The peak of the multiplicity distribution for the stan

dard Monte Carlo events

nominal efficiency 100%—dashed

line

lies at a higher value than for the data. Reducing the

simulated OM sensitivity by 50% results in a peak at lower

values than the data. The other variable strongly affected by

the OM sensitivity—the velocity of the line fit, introduced in

Sec. IV A

—is the apparent velocity of the observed light

front traveling through the ice; see Fig. 20

bottom

As a next step, we investigated the effect of the

ANGSENS

OM model

first introduced in Sec. III

on the atmospheric

neutrino Monte Carlo simulation. The results of this simula

tion gave a more consistent description of the experiment for

several variables—e.g., the hit multiplicity

the dotted line in

Fig. 20

—and they produced the absolute neutrino event pre

diction closer to what was found in Analysis I

236.9 events

predicted, 223 observed

. Similar effects are seen when this

Monte Carlo simulation is used with analysis II, however the

number of predicted events is 25% smaller than observed.

Thus the

ANGSENS model, while encouraging, does not com

pletely predict the properties of observed events in both

analyses.

Another uncertainty lies in the Monte Carlo routines used

to propagate muons through the ice and rock surrounding the

detector. A comparison of codes based on

and

indi

cates that different propagators may change the event rates

by some 25%.

Other factors include the simulation of the data acquisi

tion electronics and possible errors in the time calibrations of

individual modules. These effects have been studied by sys

tematically varying relevant parameters in the Monte Carlo

simulations. For realistic levels of variation, these effects are

well below the 10% level.

Figure 21 demonstrates how the zenith angle distribution

depends on different atmospheric neutrino event generators

our standard generator

NUSIM

and another generator

NU2MU

, and also on the chosen angular sensitivity of

the optical module. Neutrino flavor oscillations lead to a fur

FIG. 20. Distributions of two variables that are affected by the

OM sensitivity, comparing different signal Monte Carlos events to

the observed data. Top: the number of OMs hit (

); bottom: the

event velocity for a simplified fit

line fit,

linefit

FIG. 21. Distribution of simulated zenith angles for different

neutrino generators and also for a modified angular sensitivity of

the OM.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

01200517

ther reduction of the

ANGSENS

prediction by 5.4%

in par

ticular, close to the vertical direction

, assuming sin

and

2.5

30,38

. The prediction is re

duced by 11% if the largest allowed

is used.

The combined effect of all these systematic uncertainties

is sufficiently large that simulations of a given atmospheric

neutrino flux can produce predictions for the event rate vary

ing by a factor of two. By contrast, the estimated theoretical

uncertainty in the atmospheric neutrino flux, at the energies

probed by these analyses, is 30%

. The effect of neutrino

oscillations with the SuperK preferred parameters would be

less than 10% at these energies.

VIII. SYNTHESIS AND GENERAL OVERVIEW

Both analyses I and II are able to separate more than 200

neutrino event candidates from the 130.1 days of AMANDA

B10 detector lifetime in 1997. Based on atmospheric neu

trino simulations we find that about 4% of the total number

of events triggered by upward moving neutrinos passed the

final selection. A total deficit in the event rate of about 35%

with respect to the standard neutrino Monte Carlo prediction

is found for both analyses. An event overlap of 102 experi

mental events is observed, consistent with a predicted over

lap of 119

13 from the atmospheric neutrino Monte Carlo

prediction. Thus, the combined sample of data provides

about 300 neutrino candidates. Both analyses estimate their

residual background to be about 10% of the number of neu

trino event candidates.

Figure 22 shows the energy distribution of the simulated

neutrinos and the corresponding muon events. Ninety per

cent of all Monte Carlo signal events have muon

neutrino

energies between 48

GeV and 1.8

3.4

TeV. The domi

nant part of the signal events in this analysis comes from

neutrino energies below 1 TeV. Figure 23 shows the effective

area as a function of the zenith angle for two ranges of the

muon energy at the point of closest

POC

approach to the

detector. The effective area for muons with energies at POC

between 100 and 1000 GeV is 3.9

at trigger level

and 2800 m

after application of the neutrino selection cuts.

It should be noted that much higher effective areas are pos

sible when searching for neutrinos from astrophysical point

sources

or from gamma ray bursts

Figure 24 shows the point spread function of the recon

structed muon trajectory with respect to the true muon direc

tion. Based on Monte Carlo simulations, we find a median

angular resolution of muons from atmospheric neutrinos of

3.2° for the final sample. A more detailed study of the angu

lar resolution can be found in

25,34,35

. Figure 25 shows

the skyplot

equatorial coordinates

of all the candidate neu

trino events found across both analyses. The distribution of

the events on the skyplot is consistent with a random distri

bution.

IX. CONCLUSIONS

The AMANDAB10 data from 130.1 days of livetime

during the austral winter of 1997 have been analyzed in an

FIG. 22. Energy distributions for simulated atmospheric neu

trino events which pass the final neutrino cuts. The effect of neu

trino oscillations has not been taken into account. The figure shows

the neutrino and muon energies at the interaction vertex and the

energy of the muons at the point of closest approach to the detector

center.

FIG. 23. Effective area for muons versus zenith angle. The en

ergy of the muons is given at the point of closest approach to the

detector.

FIG. 24. Monte Carlo simulation of the angular resolution for

muons that pass the final selection criteria. The median error is 3.2°.

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200518

effort to detect high energy atmospheric neutrino events, and

to compare their properties to expectations. Two working

groups in the collaboration, using differing reconstruction,

cut optimization and instrumental event rejection techniques,

produced sets of 223 and 204 neutrino candidates, respec

tively. Several methods of background estimation put the re

sidual event contamination from downgoing atmospheric

muons and instrumental artifacts at about 10%. Taking into

account systematic uncertainties, the observed event num

bers are consistent with systematically varied atmospheric

neutrino Monte Carlo predictions, which are from 150–400

events. The range of these predictions is dominated by un

certainties in the neutrino flux, in the understanding of pho

ton propagation through the bulk ice and the refrozen hole

ice, and in muon propagation and energy loss. The Monte

Carlo prediction suggests that 90% of the selected events are

produced by neutrinos in the energy range of

;

66 GeV to

3.4 TeV. The observation of atmospheric neutrinos in line

with expectations establishes AMANDAB10 as a working

neutrino telescope. We finally note that many of the proce

dures for signal separation simplify considerably in larger

detectors. In particular, first results from AMANDAII

36,37

demonstrate that the neutrino signal is separated with

much higher efficiency and with fewer cuts than for

AMANDAB10.

ACKNOWLEDGMENTS

This research was supported by the following agencies:

U.S. National Science Foundation, Office of Polar Programs;

U.S. National Science Foundation, Physics Division; Univer

sity of Wisconsin Alumni Research Foundation; U.S. Depart

ment of Energy; Swedish Natural Science Research Council;

Swedish Research Council; Swedish Polar Research Secre

tariat; Knut and Alice Wallenberg Foundation, Sweden; Ger

man Ministry for Education and Research; U.S. National En

ergy Research Scientific Computing Center

supported by

the Office of Energy Research of the U.S. Department of

Energy

; UCIrvine AENEAS Supercomputer Facility; Deut

sche Forschungsgemeinschaft

DFG

. D. F. Cowen acknowl

edges the support of the NSF CAREER program and C.

rez de los Heros acknowledges support from the EU 4th

framework of Training and Mobility of Researchers.

E. Andre

et al.

, Astropart. Phys.

2000

E. Andre

et al.

, Nature

London

410

, 441

2001

AMANDA Collaboration, K. Woschnagg, in

Proceedings of

the

International Cosmic Ray Conference

IUPAP, Salt

Lake City, UT, 1999

, Vol. 2, pp. 200–203.

P. B. Price, K. Woschnagg, and D. Chrikin, Geophys. Res.

Lett.

, 2129

2000

J. Ahrens

et al.

, Astropart. Phys.

, 345

2002

S. N. Boziev

et al.

, INR Report P0630

unpublished

D. Heck

et al.

, Report FZKA 6019, Forschungszentrum

Karlsruhe, Karlsruhe, Germany

unpublished

D. Heck, in

Simulation and Analysis Methods for Large Neu

trino Telescopes

DESY, Zeuthen, Germany, 1998

, pp. 228–

234,

DESYPROC199901.

W. Lohmann, R. Kopp, and R. Voss, Report CERN8503,

Geneva, Switzerland

unpublished

R. Kopp, W. Lohmann, and R. Voss, MUDEDX: Parametriza

tion and Monte Carlo generation of energy loss of high energy

muons

1–10000 GeV

; for astrophysicists up to 100000 GeV,

Version 2.02, 1995

private communication

P. Lipari and T. Stanev, Phys. Rev. D

, 3543

1991

W. Rhode and D. Chirkin, in

Proceedings of the

Interna

tional Cosmic Ray Conference

Copernicus Gesellschaft, Ham

burg, Germany, 2001

, Vol. 3, pp. 1017–1020.

B. WiebelSooth and P. L. Biermann,

Numerical Data and

Functional Relationships in Science and Technology

, Landolt

rnstein, New Series, Vol. VI 3C

SpringerVerlag, Berlin,

Heidelberg, 1998

, Chap. 7.6, pp. 37–90.

A. Karle, in

Simulation and Analysis Methods for Large Neu

trino Telescopes

Ref.

, pp. 174–185,

DESYPROC199901.

S. Hundertmark, Ph.D. thesis, Humboldt Universita

t zu Berlin,

Berlin, Germany, 1999, available at URL

http://amanda.berkeley.edu/manuscripts/

S. Hundertmark, in

Simulation and Analysis Methods for Large

Neutrino Telescopes

Ref.

, pp. 276–286,

DESYPROC1999

G. C. Hill, Astropart. Phys.

, 215

1997

G. C. Hill, Ph.D. thesis, University of Adelaide, Adelaide, Aus

tralia, 1996.

P. Lipari, Astropart. Phys.

, 195

1993

J. Ahrens

et al.

unpublished

V. Stenger, DUMAND Internal Report HDC190.

C. Wiebusch, in

Simulation and Analysis Methods for Large

Neutrino Telescopes

Ref.

, pp. 302–316,

DESYPROC1999

D. Pandel, Diploma thesis, HumboldtUniversity, Berlin, 1996.

G. C. Hill, in

Proceedings of the

International Cosmic

Ray Conference

Ref.

, Vol. 3, pp. 1279–1282.

A. Biron, Ph.D. thesis, Humboldt Universtita

t zu Berlin, Ber

lin, Germany, 2002, available at URL

FIG. 25. Neutrino skyplot of upgoing events as seen with

AMANDAB10 in 1997 in equatorial coordinates. In this figure,

neutrino events from both analyses are combined. The background

of nonneutrino events is estimated to be less than 10%.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC... PHYSICAL REVIEW D

, 012005

2002

01200519

http://amanda.berkeley.edu/manuscripts/

T. R. DeYoung, Ph.D. thesis, University of Wisconsin, Madi

son, 2001, available at URL

http://amanda.berkeley.edu/manuscripts/

M. Gaug, Diploma thesis, Humboldt Universita

t zu Berlin,

Berlin, Germany, 2001,

DESYTHESIS2001022, available at URL

http://amanda.berkeley.edu/manuscripts/.

AMANDA Collaboration, A. Bouchta, in

Proceedings of the

26th International Cosmic Ray Conference

Ref.

,HE

3.2.11.

E. Dalberg, Ph.D. thesis, Stockholm University, Stockholm,

Sweden, 1999, available at URL

http://amanda.berkeley.edu/manuscripts/

SuperKamiokande Collaboration, J. Kameda, in

Proceedings

of the

International Cosmic Ray Conference

Ref.

Vol. 3, pp. 1057–1060.

T. K. Gaisser, ‘‘Uncertainty in flux of Atmospheric Neutrinos:

Implications for Upward Muons in Amanda B10,’’ Internal

Report 20001201, 2000.

J. Ahrens

et al.

, ‘‘Search for point sources of high energy neu

trinos with the AMANDA detector.’’

AMANDA Collaboration, R. Hardtke and G. Barouch, in

Pro

ceedings of the

International Cosmic Ray Conference

Ref.

, Vol. 3, pp. 1121–1124.

AMANDA Collaboration, ‘‘Calibration and Survey of

AMANDA with the SPASE detectors’’

to be published

AMANDA Collaboration, G. Spiczak, in

Proceedings of the

International Cosmic Ray Conference

Ref.

, Vol. 3,

pp. 977–980.

AMANDA Collaboration, R. Wischnewski, in

Proceedings of

the

International Cosmic Ray Conference

Ref.

, Vol.

3, pp. 1105–1108.

AMANDA Collaboration, S. W. Barwick, in

Proceedings of

the

International Cosmic Ray Conference

Ref.

, Vol.

3, pp. 1105–1108.

S. Fukuda

et al.

, Phys. Rev. Lett.

, 3999

2000

J. AHRENS

et al.

PHYSICAL REVIEW D

, 012005

2002

01200520