56513 1040..1057

SEARCH FOR POINT SOURCES OF HIGH-ENERGY NEUTRINOS WITH AMANDA

J. Ahrens,

X. Bai,

G. Barouch,

S. W. Barwick,

R. C. Bay,

T. Becka,

K.H. Becker,

D. Bertrand,

F. Binon,

A. Biron,

S. Boeser,

O. Botner,

A. Bouchta,

8,10

O. Bouhali,

T. Burgess,

S. Carius,

T. Castermans,

D. Chirkin,

5,6

J. Conrad,

J. Cooley,

D. F. Cowen,

A. Davour,

C. De Clercq,

T. DeYoung,

P. Desiati,

J.P. Dewulf,

P. Doksus,

J. Edsjo

P. Ekstro

T. Feser,

T. K. Gaisser,

M. Gaug,

L. Gerhardt,

A. Goldschmidt,

A. Hallgren,

F. Halzen,

K. Hanson,

R. Hardtke,

T. Hauschildt,

M. Hellwig,

P. Herquet,

G. C. Hill,

P. O. Hulth,

K. Hultqvist,

S. Hundertmark,

J. Jacobsen,

A. Karle,

J. Kim,

L. Ko

pke,

M. Kowalski,

K. Kuehn,

J. I. Lamoureux,

H. Leich,

M. Leuthold,

P. Lindahl,

J. Madsen,

P. Marciniewski,

H. Matis,

C. P. McParland,

T. C. Miller,

2,18

Y. Minaeva,

P. Miocinovic

P. C. Mock,

4,19

R. Morse,

T. Neunho

ffer,

P. Niessen,

D. R. Nygren,

H. O

gelman,

P. Olbrechts,

C. Pe

rez de los Heros,

A. C. Pohl,

P. B. Price,

G. T. Przybylski,

K. Rawlins,

E. Resconi,

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,

M. Solarz,

G. M. Spiczak,

C. Spiering,

D. Steele,

P. Steffen,

R. G. Stokstad,

K.H. Sulanke,

I. Taboada,

L. Thollander,

S. Tilav,

C. Walck,

C. Weinheimer,

C. H. Wiebusch,

8,10

C. Wiedemann,

R. Wischnewski,

H. Wissing,

K. Woschnagg,

W. Wu,

G. Yodh,

and S. Young

(The AMANDA Collaboration)

Received 2002 July 26; accepted 2002 October 2

ABSTRACT

This paper describes the search for astronomical sources of high-energy neutrinos using the

AMANDA-B10 detector, an array of 302 photomultiplier tubes used for the detection of Cerenkov light

from upward-traveling neutrino-induced muons, buried deep in ice at the South Pole. The absolute pointing

accuracy and angular resolution were studied by using coincident events between the AMANDA detector

and two independent telescopes on the surface, the GASP air Cerenkov telescope and the SPASE extensive

air shower array. Using data collected from 1997 April to October (130.1 days of live time), a general survey

of the northern hemisphere revealed no statistically significant excess of events from any direction. The

sensitivity for a flux of muon neutrinos is based on the effective detection area for through-going muons.

Averaged over the northern sky, the effective detection area exceeds 10,000 m

for

10 TeV. Neutrinos

generated in the atmosphere by cosmic-ray interactions were used to verify the predicted performance of the

detector. For a source with a differential energy spectrum proportional to

and declination larger than

+40

, we obtain

Þ?

GeV cm

for an energy threshold of 10 GeV.

Subject headings:

neutrinos — surveys

On-line material:

color figures

Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.

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

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

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

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

Fachbereich 8 Physik, BUGH Wuppertal, D-42097 Wuppertal, Germany.

Universite

Libre de Bruxelles, Science Faculty CP 230, Boulevard du Triomphe, B-1050 Brussels, Belgium.

DESY-Zeuthen, D-15735 Zeuthen, Germany.

Division of High Energy Physics, Uppsala University, S-75121 Uppsala, Sweden.

Current address: CERN, CH-1211 Geneva 23, Switzerland.

Fysikum, Stockholm University, S-11385 Stockholm, Sweden.

Department of Technology, University of Kalmar, S-39182 Kalmar, Sweden.

University of Mons-Hainaut, Mons, Belgium.

Department of Physics, Pennsylvania State University, University Park, PA 16802.

Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium.

Lawrence Berkeley National Laboratory, Berkeley, CA 94720.

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

Current address: Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723.

Current address: Optical Networks Research, JDS Uniphase, 100 Willowbrook Road, Freehold, NJ 07728-2879.

Departamento Fı

sica, University Simo

n Bolı

var, Caracas, Venezuela.

The Astrophysical Journal

, 583:1040–1057, 2003 February 1

1040

1. INTRODUCTION

Nature provides precious few information carriers from

the deep recesses of space, and it is imperative to develop

techniques to exploit each one. Throughout history, the

photon messenger has made vital contributions to the

understanding of the observable universe. In this paper, we

present results from a new generation of telescopes designed

to detect a very different kind of information carrier, high-

energy neutrinos (where

1 TeV). The search for

astronomical sources of high-energy neutrinos is one of the

central missions of the Antarctic Muon and Neutrino

Detector Array (AMANDA; Wischnewski et al. 1999). In

this paper, we describe a general search for continuous emis-

sion from a spatially localized direction in the northern

sky,

restricted to declinations greater than +5

. The search

technique is conceptually simple: a point source is identified

by a statistically significant enhancement over expected

background fluctuations from a particular direction.

Expected background is readily obtained experimentally

from off-source sky bins within the same band of declina-

tion. In contrast, unresolved, or diffuse, signals are charac-

terized by an isotropic distribution, and backgrounds are

estimated by detector simulation programs. The most favor-

able flux predictions for point sources are several orders of

magnitude lower than the most optimistic predictions for

diffusely distributed sources. However, atmospheric neu-

trino background is diffusely distributed as well, so the level

of intrinsic background in the diffuse search is also several

orders of magnitude higher. While signal-to-noise ratio con-

siderations favor the search for diffuse emission over point-

source searches, the interpretation of a diffusely distributed

signal is more ambiguous. Thus, the search for point sources

complements the search for diffuse sources. The latter

search is described in Hill & Leuthold (2001).

The more

specific searches for point emission from gamma-ray

bursters (Hardtke & Barouch 2001)

and quasi-pointlike

emission from Galactic dark matter trapped in the core of

the Earth (Ahrens et al. 2002b) are presented in separate

papers since these analyses were optimized for different flux

spectra and different background characteristics.

2. MOTIVATION

The origin of cosmic rays is one of the oldest puzzles in

particle astrophysics. Shocks from Galactic supernovae are

widely believed to accelerate cosmic rays to

eV, while

the sources of cosmic rays at the most extreme energies are

not known. Plausible models of particle acceleration exist

for many classes of Galactic and extragalactic objects, but

supporting evidence for any model is largely circumstantial.

The observation of high-energy neutrinos from point

sources would unequivocally confirm the hadronic nature

of such accelerators. Unfortunately, the predicted neutrino

fluxes from Galactic and extragalactic point sources are

too low to be detected with AMANDA-B10, although

uncertainties in the model parameters lead to considerable

variation in the flux predictions.

Supernova remnants (SNRs) are one of the few classes of

Galactic sites that have the capability to supply sufficient

power to accelerate Galactic cosmic rays. The diffusive

shock mechanism naturally produces a power-law spectrum

, which is consistent with the deduced

spectral index of cosmic rays.

Recent observations of TeV gamma rays from plerions

such as the Crab Nebula and SNRs provide direct evidence

for particle acceleration to high energies. However, these

observations do not provide compelling evidence for

hadronic

acceleration because of an unfortunate ambiguity:

it is possible (and even probable) that electrons are solely

responsible for the high-energy gamma-ray production. But

if SNRs are the accelerators of Galactic cosmic rays, they

must also accelerate hadrons. A class of models exploits this

idea by suggesting that both protons and electrons are accel-

erated by the supernova shock. Pions, both neutral and

charged, are produced in the nuclear collisions between pro-

tons and ambient material (a cosmic equivalent of a ‘‘ beam

dump ’’ commonly used by terrestrial accelerators) and then

decay to high-energy gamma rays and neutrinos.

While the notion of particle acceleration by supernova

shocks provides a credible and largely consistent picture,

not all observations neatly fit this scheme. Alternative sites

for cosmic-ray acceleration may emerge from a detailed

study of the neutrino sky. For example, Galactic microqua-

sars, a subclass of X-ray binary systems that exhibit relativ-

istic radio jets, have been identified as possible sources of

high-energy neutrino emission (Levinson & Waxman 2001)

and potential sources of the highest energy cosmic rays. If

they accelerate cosmic rays to high energies, then their dense

environment creates suitable conditions for an efficient

beam dump.

Turning to extragalactic sources, active galactic nuclei

(AGNs) are among the most luminous objects in the uni-

verse and promising sources of neutrinos. In these models,

high-energy neutrino fluxes are generated near the central

engine or in the jets of radio-loud AGNs (e.g., blazars, a

class of objects where the jet intersects the line of sight of the

observer). The fact that gamma-ray emission has been

detected (Cantanese & Weekes 1999) from nearby blazars

Mrk 421 and Mrk 501 provides strong evidence for particle

acceleration to high energies.

The time-averaged energy

spectrum from Mrk 501 during 1997 is consistent with an

unbroken power-law energy spectrum up to 10 TeV

(Weekes 2001; Konopelko et al. 1999). Beam dump models

of neutrino production predict comparable fluxes of

gamma-ray photons and neutrinos. However, gamma-ray

photons at TeV energies may interact with material or pho-

ton fields in the source or interact with the diffuse infrared

background photons during their flight. Because of this

reprocessing, the measured energy spectrum for gamma-ray

photons may not trace the energy spectrum of the source.

Consequently, it is possible for the ratio of neutrino flux to

gamma-ray flux from a given source to exceed unity. Con-

straints on this ratio are discussed in

Recently, it has been argued (Buckley et al. 1998a, 1998b)

that the rapid time variability of high-energy photon

Although the flux limits reported in this paper are computed assuming

continuous emission, upper bounds could be generated for periodic or

episodic emission as well.

Available at http://area51.berkeley.edu/manuscripts/

20010604xx-diffuse-sens.pdf.

Available at http://area51.berkeley.edu/manuscripts/

20010606xx-grbdoc.pdf.

The review by Cantanese & Weekes (1999) presents a current list of

detected very high energy gamma-ray sources.

SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1041

emission from AGN blazars and the correlated variation

between the X-ray and TeV regimes disfavor hadronic

acceleration models for this particular class of objects, but

others have shown that rapid and correlated variability can

be accommodated by modest extensions to the existing

hadronic acceleration models (Rachen 2000; Dermer 1999).

The vigorous debate suggests that high-energy neutrino

detectors can play a central role in deciphering the accelera-

tion mechanism.

Figure 1 provides a survey of model predictions for

fluxes of high-energy neutrinos. The models were selected

to highlight the variation in spectral characteristics. The

line labeled 3C 273 is representative of several recent neu-

trino flux predictions, e.g., a similar differential flux is

predicted for microquasars (Distefano et al. 2002) in the

region of sky visible to AMANDA and the flat-spectrum

radio quasar 3C 279 (Dermer & Atoyan 2001). The figure

also shows the differential neutrino flux limit for an

assumed source spectrum proportional to

for

AMANDA-B10 and the anticipated corresponding sensi-

tivity of AMANDA-II and IceCube (Karle et al. 2003).

The AMANDA-B10 result, the subject of this paper, is

valid for declinations greater than +40

. Many theoreti-

cal models of potential astronomical neutrino sources

predict a very hard energy spectrum, approximately

(Learned & Mannheim 2000), which leads to a most

probable energy for a detected neutrino well above 1

TeV (typically 10–30 TeV). This high energy is a conse-

quence of three facts: the neutrino cross section for weak

interactions increases with neutrino energy, and the prop-

agation length of the secondary muon increases and the

effective detection area increases as light emission along

the muon track increases with energy.

Even though the cosmic-ray puzzle provides a powerful

motivation to explore the sky for neutrino emission, not all

high-energy neutrino sources need to contribute to the

cosmic-ray flux. In particular, a powerful accelerator may

be surrounded by too much material to emit high-energy

photons or cosmic rays (they would interact and cascade

down to lower energies), but this accelerator could be dis-

covered by exploiting the neutrino messenger. Several

models of such ‘‘ hidden ’’ sources have appeared in the liter-

ature. For example, the predicted flux of neutrinos from

pre-AGN objects (Berezinsky & Dokuchaev 2001) leads to

a muon detection rate of

10 yr

3. DESCRIPTION OF THE AMANDA DETECTOR

The AMANDA telescope is located below the surface of

the Antarctic ice sheet at the geographic South Pole. The

neutrino detection technique relies on the detection of Cer-

enkov light from upward-traveling neutrino-induced

muons. Figure 2 shows the current configuration of the

AMANDA detector. The shallow array, AMANDA-A,

was deployed to depths between 800 and 1000 m in an

exploratory phase of the project. The deeper array of 10

strings, referred to as AMANDA-B10, was deployed during

the austral summers between 1995 and 1997, to depths

between 1500 and 2000 m. At this depth, the optical proper-

ties are suitable for track reconstruction (Woschnagg et al.

(dN/dE) [GeVcm

]

[GeV]

AMANDAII (1 yr l.t.)

AMANDAB10 (this work)

IceCube

3C273

Crab

AGN Core

Mkn 501 (

)

Atm.

Fig.

—Representative survey of

flux predictions from cosmic

accelerators of high-energy neutrinos. The AMANDA-B10 result is pre-

sented here. The dashed horizontal lines give preliminary estimates of the

minimum detectable flux by AMANDA-II after 1 yr of live time (Barwick

et al. 2001) and IceCube (Spiering 2001). The atmospheric neutrino fluxes

(Agrawal et al. 1996) are appropriate for a circular patch of 1

(

lower curve

)

and 3

radius. The curves do not include the normalization uncertainty,

possibly 30% in magnitude (Gaisser 2002; T. K. Gaisser 2002, private com-

munication). Models: 3C 273 (Nellen, Mannheim, & Biermann 1993), Crab

model I (Bednarek & Protheroe 1999), AGN core (Stecker & Salamon

1996), and Mrk 501 assuming neutrino spectrum is identical to observed

gamma spectrum during flaring phase (Weekes 2001). [

See the electronic

edition of the Journal for a color version of this figure.

]

120 m

snow layer

optical module (OM)

housing

pressur

Optical

Module

silicon gel

HV divider

light diffuser bal

60 m

AMANDA as of 2000

zoomed in on one

(true scaling)

200 m

Eiffel Tower as comparison

Depth

surface

50 m

1000 m

2350 m

2000 m

1500 m

810 m

1150 m

AMANDAA (top)

zoomed in on

AMANDAB10 (bottom)

AMANDAA

AMANDAB10

main cable

PMT

Fig.

—Schematic view of the AMANDA neutrino telescope. This

paper describes an analysis of data taken in 1997 with AMANDA-B10, the

10 inner strings shown in the expanded view in the center. Each dot

represents one optical module in the array. [

See the electronic edition of the

Journal for a color version of this figure.

]

1042 AHRENS ET AL. Vol. 583

1999).

The strings are arranged in a circular pattern when

viewed from the surface. The instrumented volume of

AMANDA-B10 forms a vertical cylinder with a diameter of

120 m. Most electronics are housed on the surface in a

research facility located within a kilometer of the Amundsen-

Scott South Pole Station. The detector was commissioned in

1997 February (Wischnewski et al. 1999; Barwick et al. 2000)

and expanded by adding nine strings of optical modules

(OMs) between 1997 December and 2000 January. The com-

posite array of 19 strings forms the AMANDA-II array,

which was commissioned in 2000 February.

AMANDA-B10 consists of 302 OMs arranged on 10 ver-

tical strings. Each OM contains an 8 inch (21 cm) diameter

photomultiplier tube (PMT) controlled by passive elec-

tronics and housed in a glass pressure vessel. The OMs are

connected to the surface by dedicated electrical cables,

which supply high voltage and carry the anode signals from

the PMTs. For each event, the amplitudes and arrival times

of the pulses from the OMs are digitized by peak analog-to-

digital converter and time-to-digital converter (TDC) val-

ues. The TDCs are capable of measuring eight distinct

pulses per channel. The precision of the arrival time mea-

surement is 5 ns. Details of deployment, timing resolution,

and detector operation can be found in Andres et al. (2000,

2001). Readout of the entire array was triggered by a major-

ity logic system, which demanded that at least 16 OMs pro-

duce signals, or ‘‘ hits,’’ within a time window of 2.2

s. This

window takes into account the rather large time variation

introduced by the large geometric size of the detector and

the cable propagation delays. Random signals from the

OMs (or ‘‘ noise ’’) were observed at a rate of 300 Hz on the

inner four strings and 1.5 kHz for OMs on the outer six

strings, the difference being due to different levels of radio-

active potassium in the glass pressure vessels. On average,

random noise contributed one count per event to the major-

ity trigger.

Optical absorption and scattering properties of the glacial

ice that encapsulates the AMANDA detector have been

studied using light sources buried with the strings and

Cerenkov light from atmospheric muons. These studies

(Woschnagg et al. 1999) confirm that the ice is not homoge-

neous but consists of horizontal strata correlated with cli-

matological events in the past, such as ice ages.

Variations

in the concentration of insoluble impurities between the

strata produce a strong modulation of the optical proper-

ties. The absorption length, averaged over depth within the

AMANDA-B10 array, is 110 m at a wavelength of 400 nm,

and the average effective scattering length is approximately

20 m.

The detection of neutrinos relies on the observation of

Cerenkov photons generated by muons created in charged-

current interactions. At the energies of interest, muons typi-

cally propagate for distances in excess of several kilometers

(e.g., a muon with

10 TeV will travel 8 km in water).

Therefore, neutrino interactions outside the instrumented

volume can be inferred by the presence of a muon, providing

a method to extend the volume of the detector beyond the

instrumented boundary of the array. The average angle

between the muon direction and the parent neutrino direc-

tion,

, is approximately 0

TeV

for

less

than 100 TeV (Oppelt 2001).

However, nearly independ-

ent of the muon energy, the precision of the measured muon

direction in AMANDA-B10 is approximately 4

(see

6),

which dominates the angular uncertainty in the neutrino

direction.

The AMANDA-B10 data analyzed here were collected

between 1997 April and October. Once construction was

completed in 1997 February, calibration and data manage-

ment activities continued until April. Operations ceased

between 1997 late October and 1998 February, because of

the beginning of construction of the AMANDA-II array.

Furthermore, limitations in the data acquisition and archiv-

ing system during that first year of operation reduced the

total live time to approximately 130.1 days.

4. SIMULATIONS

Astronomical signals are unlikely to produce more than a

few tens of upgoing neutrino events per year in AMANDA-

B10. Data are therefore overwhelmingly dominated by two

types of background: downgoing atmospheric muons gener-

ate essentially all of the recorded events, and atmospheric

neutrinos contribute a few tens of events per day. The point-

source search relies on a good understanding of both signal

and background through simulations based on Monte

Carlo techniques.

Atmospheric muon events are generated from the mea-

sured flux of cosmic rays (Wiebel-Sooth & Biermann 1998).

Two different air shower simulation packages were used to

assess systematic uncertainty: BASIEV (Bosiev et al. 1989)

and CORSIKA (Version 5.6; Heck et al. 1998, 1999) using

the QGSJET hadronic interaction model. CORSIKA was

modified to include the curved geometry of the Earth and

atmosphere to provide a more accurate description of the

flux at zenith angles close to the horizon. Most characteris-

tics of the events generated with BASIEV were found to be

similar to those from the more accurate but computation-

ally more intensive CORSIKA simulation. The density pro-

file of the atmosphere was modified for polar conditions,

but no attempt was made to replicate the small seasonal var-

iations of the trigger rate (Bouchta et al. 1999).

Muon

tracking from the surface to the detector was handled by the

muon propagation program MUDEDX (Lohmann, Kopp,

& Voss 1985; W. Lohmann, R. Kopp, & R. Voss 1995, pri-

vate communication [MUDEDX Version 2.02]), and the

energy-loss characteristics were compared against two addi-

tional propagation programs that are available for general

use: PROPMU (Lipari & Stanev 1991) and MMC (Rhode

& Chirkin 2001). Integral lateral distributions of muons at

the depth of AMANDA were simulated for proton and iron

showers (X. Bai et al. 2003, in preparation) and used for ver-

ification of the detector performance as described below.

The propagation of upward-traveling muons from neu-

trino interactions was treated differently from that of down-

going atmospheric muons because the energies of signal

neutrinos were expected to extend to much higher energies.

Available at http://krusty.physics.utah.edu/~icrc1999/root/vol2/

h4_1_15.pdf.

See P. B. Price, K. Woschnagg, & D. Chirkin (2000), AMANDA

public manuscript 20000201, available at http://amanda.berkeley.edu/

manuscipts.

Available at http://www-zeuthen.desy.de/~apohl/files/doktor/ps.gz.

Available at http://krusty.physics.utah.edu/~icrc1999/root/vol2/

h3_2_11.pdf.

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1043

Neutrinos were tracked through the Earth and allowed to

interact in the ice within or near the instrumented volume of

the detector or in the bedrock below (Hill 1997). Muons

with energies above 10

GeV at production were propa-

gated using PROPMU until they reached the rock-ice boun-

dary and then propagated through the ice in exactly the

same way as downgoing atmospheric muons. For energies

below 10

GeV at the production vertex, muons were

tracked with MUDEDX. The background fluxes from at-

mospheric

and

(Agrawal et al. 1996) were included

(AMANDA cannot differentiate the charge sign of the

muon).

In addition to background from atmospheric muons and

muon neutrinos, the detection efficiency for atmospheric

electron neutrinos has been simulated. At the relevant ener-

gies, the flux of

is far smaller than for

, so the back-

ground contribution is small a priori. Furthermore, the

topology of electron neutrino events, reflecting the electro-

magnetic shower generated by the secondary electron, is

spherical rather than linear, and this characteristic has been

exploited to further increase the rejection. Simulations show

that the detection rate of atmospheric

in the point-source

analysis is only 0.3% of

(Young 2001)

and therefore

negligible in this context. We note that a separate analysis

was devised to search for electron neutrinos and conse-

quently achieved a much larger sensitivity (Ahrens et al.

2002c).

An overview of the simulation of the detector response is

given in Hundertmark (1999). The depth dependence of the

optical properties of the bulk ice (Woschnagg et al. 1999)

is included along with a realistic treatment of trigger condi-

tions, intrinsic noise rates, and hardware-dependent pulse

shapes. The linearity and saturation of the photomultiplier

response is included. The angle-dependent sensitivity of the

optical module was computed from a convolution of PMT

quantum and collection efficiencies as estimated by the man-

ufacturer, detection efficiency, wavelength-dependent trans-

parency through the pressure housing and buffer gel, and

obscuration by cables and mechanical support hardware.

The relative angular dependence of the sensitivity of the

photomultiplier tubes was measured in the laboratory. The

local optical properties of the refrozen ice were included in

the photon tables that describe the probability and the tim-

ing characteristics of photon propagation (Ahrens et al.

2002a).

Figure 3 presents the differential distribution of the multi-

plicity of optical modules, or channels, participating in an

event,

, for the full detector simulation and for experi-

mental data after known detector-related artifacts were

removed. The integrated rates differ by less than 25%, which

is within the systematic uncertainties associated with the

flux of the primary cosmic rays (Gaisser 2002; T. K. Gaisser

2002, private communication) and uncertainties associated

with the absolute sensitivity of the optical module (see

8).

The agreement in the shape of the distribution demonstrates

a good understanding of the overall sensitivity of the array

for the most common events that trigger AMANDA-B10.

As the inset of Figure 3 shows, the largest values of

are produced by events with more than one muon. This

information provides indirect evidence that the response of

AMANDA to single high-energy muons is correctly mod-

eled, by the following argument. Multimuon bundles that

reach AMANDA mainly consist of muons below the critical

energy of 600 GeV, which implies that energy loss due to

ionization is near minimum. The Cerenkov light production

from muons well above the critical energy is dominated by

electromagnetic showers, and the total light from a muon

with

is approximately equal to the light of a bundle of

muons, where

crit

. Therefore, the light production

by a multimuon event can be related to the light production

by a single-muon event. For example, the average energy

loss per unit length for a muon with energy 10

eV is

approximately a factor of 15 larger than for a single muon,

as long as the energy is below 600 GeV. There are several

modest limitations to this line of reasoning. One is that the

lateral distribution of multimuon events generates Ceren-

kov photons over a much larger cylinder than a single

muon. Another difference is that multimuon events deposit

Cerenkov photons more uniformly than the equivalent

high-energy muon, for which energy loss is dominated by

occasional pair production and bremsstrahlung. However,

optical scattering by the ice mitigates the effects of nonuni-

form photon generation. Simulations show that bundles of

20 muons generate an

distribution similar to that of

single muons with an energy of 10 TeV. The correlation

between muon multiplicity and

multiplicity is shown in

Figure 4. Note that bias introduced by the majority logic in

the trigger prevents the muon multiplicity from converging

to zero as

approaches zero.

Available at http://area51.berkeley.edu/manuscripts/

20010702xx-young-main.pdf.

Available at http://krusty.physics.utah.edu/~icrc1999/

proceedings.html.

Differential Rate [Hz]

experiment (99 Hz)

simulation (77 Hz)

Relative Frequency

single

multi

0 20 40 60 80 100 120 140

0 50 100

Fig.

—Differential distribution of observed (

solid curve

) and predicted

(

dashed curve

) trigger rates as a function of the event multiplicity

(i.e.,

the number of optical modules that participate in each event). The inte-

grated rates are given in parentheses. Note that

extends below the

majority logic threshold of 16 because of removal of data caused by experi-

mental artifacts.

Inset

: Relative contribution to the trigger rates from single

muons (

solid curve

) and multiple-muon bundles (

dashed curve

) that traverse

the fiducial volume of the array. [

See the electronic edition of the Journal for

a color version of this figure.

]

1044 AHRENS ET AL. Vol. 583

5. ANALYSIS PROCEDURE

The analysis procedure exploits two essential characteris-

tics of the signal to simplify the analysis relative to atmo-

spheric neutrino measurements. First, the sources are

assumed to be point sources in the sky, so only events within

a restricted angular region are considered. Second, we use

the topological and directional characteristics of the spec-

trally hard neutrino signal to help reject poorly recon-

structed atmospheric muons (i.e., downward-traveling

muons reconstructed as upward traveling) and atmospheric

neutrinos, both of which have softer spectra. Unlike many

neutrino detectors, the effective sensitivity of AMANDA

varies dramatically as a function of the background-

rejection requirements. By concentrating on harder spectra,

the effective area of the detector can be increased by relaxing

the background-rejection criteria. Since the point-source

analysis tolerates a larger background (

) contamination in

the final data sample, the analysis procedure optimizes on

signal to noise (

ffiffiffiffi

) rather than signal purity (

Prior to track reconstruction and event selection, experi-

mental data were selected from runs that exhibited no

abnormal behavior, and various instrumentally induced

artifacts were removed. Once the data in the runs were certi-

fied, individual OMs in the array were examined to insure

proper operation. OM channels with hardware malfunction

(

15% of OMs), such as pickup from unusually large exter-

nal noise sources or fluctuations in the response of the

amplifier electronics, were rejected. Approximately 85% of

OMs remained after deselection. Occasional signals induced

by cross talk in the electrical cables or surface electronics

exhibited characteristic behavior and could be removed by

straightforward restrictions on pulse amplitude and width.

Noise signals generated internally by the photomultiplier

tubes were readily removed if their time of arrival occurred

earlier than 5 ms prior to the formation of the event trigger.

The reconstruction programs stochastically account for

PMT noise within the event duration.

After this initial data cleaning, a number of event recon-

struction techniques (Andres et al. 2000) are applied to the

data. The most sophisticated technique relies on a search in

multiparameter space to find the maximum likelihood for a

track hypothesis given the recorded hits. After reconstruc-

tion is completed, events are selected according to a set of

criteria that retain only the highest quality events that pos-

sess topological and directional information consistent with

those expected for upgoing neutrino-induced muons. In a

first step, the data sample of 1

events at trigger

level is reduced to a more manageable size by two filtering

stages. Most events in data are readily identified as due to

downward-traveling muons by computationally fast recon-

struction routines. Removing these events reduces the data

approximately by a factor of 10

An iterative analysis procedure was developed to maxi-

mize

ffiffiffiffi

for a simulated signal with an energy spectrum

proportional to

. It ignored the absolute time of the

event, which helped to minimize bias from potential sources

in the data. In this optimization the background was deter-

mined from experimental data by assuming that the fraction

of signal events in the data sample is negligible. After the fil-

tering stages, cuts were applied sequentially on a set of selec-

tion variables, with several variables included more than

once. The specific value for each cut after stage 2 was chosen

to retain

80% of the signal. At each stage, given this

constraint on signal efficiency, the same cut was made on

data for the variable with the largest rejection power,

sig

bgr

, where

pass

, and

and

pass

are the

numbers of events before and after the application of the

selection cut, respectively. The signal-to-noise ratio was

then computed as a function of zenith angle to ensure that

the acceptance of AMANDA-B10 remained as large as pos-

sible near the horizon. The effective areas for detection of

background and signal needed for this computation were

determined from simulations (as described in

7). After

each stage, this procedure was repeated on the remaining

variables.

Besides restrictions on the reconstructed zenith angle

the most effective selection criteria impose a threshold on

the number

dir

of only slightly scattered, or ‘‘ direct,’’ pho-

tons (i.e., photons that travel between the reconstructed

track and the OM in nearly a straight line) and the track

length

dir

over which these photons are detected. Further-

more, the analysis requires a minimum goodness-of-fit value

from the maximum likelihood procedure. Other criteria

evaluate the topological distribution of the photon emission

using variables that describe the granularity of the light pat-

tern along the trajectory and a related observable that

assesses the sphericity of the photon pattern.

Table 1

shows the selection variables and cuts used in this analysis,

including a brief technical description of the two filtering

stages. The selection variables were introduced previously

(Ahrens et al. 2002a), and a complete description is also

available (Young 2001). Also shown in the table are efficien-

cies and rejection factors at each stage of the analysis for

experimental data, simulated background, and simulated

signal, averaged over all angles.

Muons normally generate a linear distribution of Cerenkov

photons, whereas electromagnetic cascades initiated by pair production or

bremsstrahlung produce spherically symmetric distributions.

0 20 40 60 80 100 120

Fig.

—Muon multiplicity

vs. OM multiplicity

from a full

detector simulation. The area of the boxes is linearly proportional to num-

ber of events. The average values (

dots

) show the correlation between these

two quantities, and the vertical error bars show the statistical uncertainty.

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1045

The simulated background from atmospheric muons and

neutrinos is compared to data at all stages of the analysis to

establish confidence in the simulation. Figure 5 shows the

comparison at stage 4, which is sufficiently early in the anal-

ysis to retain high statistical precision. All distributions are

equally normalized because the optimized cut value depends

on the fraction of events that remain (

bottom panel

Figure 6 shows the final stage (13) of the analysis procedure.

We note that the signal sensitivity determined from simula-

tions is quite robust against small deviations between the

simulated event distribution and the actual response of the

detector (Young 2001).

Because of the large experimental data sample, precision

studies of detector performance are possible from the most

common events in the sample to extremely rare compo-

nents. The predicted and experimental sample sizes are com-

pared through all stages of the analysis to establish the

absolute calibration of detector sensitivity. This method

assumes that signal from astronomical sources contributes

negligibly to the sample. Figure 7 shows that the simulated

background and data agree to within a factor of 2 at all

stages of the analysis even though the size of the event sam-

ples varies by 6 orders of magnitude. The relative rates and

the agreements in shape of the selection variable distribu-

tions provide evidence that the background generators and

detector simulation programs are an adequate description

of the detector physics, including detector response.

Because of the optimization on signal to noise, all stages of

the analysis produce event samples that are dominated by

poorly reconstructed downgoing atmospheric muon events.

Diffuse backgrounds from atmospheric neutrinos become

noticeable only after rejecting most of the poorly recon-

structed atmospheric muons, but they never dominate the

event sample.

Obviously, atmospheric muon data are an imperfect tool

to investigate the sensitivity of the detector to neutrino-

induced muons, because of the downgoing nature of the

events and differences in the energy and multiplicity distri-

butions. This concern is addressed by the measurement of

atmospheric neutrinos (Andres et al. 2001; Ahrens et al.

2002a), which were used to verify the basic operational sen-

sitivity of AMANDA-B10 to a known neutrino signal. In

TABLE 1

Description of Variables Used in Analysis

Stage Selection Cut

data

bgr

sig

data

bgr

0..................... Trigger 1 1 1

. . . ...

1..................... Filter 1: 0.0193 0.0190 0.433 22.4 22.8

1a...................

... . . . ... . . . ...

1b...................

... . . . ... . . . ...

1c ...................

dir

... . . . ... . . . ...

2..................... Filter 2: 0.0232 0.0283 0.538 23.2 19.0

2a...................

... . . . ... . . . ...

2b...................

mrl

... . . . ... . . . ...

2c ...................

dir

75 m

... . . . ... . . . ...

2d...................

... . . . ... . . . ...

2e ...................

... . . . ... . . . ...

3..................... cos

1 0.867 0.861 0.925 1.07 1.07

4.....................

down

2 0.212 0.178 0.817 3.85 4.59

5.....................

02 0.370 0.334 0.947 2.56 2.84

6.....................

Phit

33 0.458 0.408 0.927 2.02 2.27

7.....................

dir

100 m 0.638 0.657 0.932 1.46 1.42

8.....................

dir

3 0.737 0.710 0.912 1.24 1.28

9.....................

mrl

26 0.711 0.671 0.912 1.28 1.36

10...................

dir

40 m 0.744 0.698 0.955 1.28 1.37

11...................

2 0.581 0.562 0.921 1.59 1.64

12...................

9 0.515 0.466 0.906 1.76 1.94

13...................

dir

9 0.659 0.616 0.963 1.46 1.56

Notes.

—Description of selection criteria applied to reconstruction variables in the data

reduction procedure. For additional information on the filters and selection variables, consult

Young (2001). The numerical identification (superscript in parentheses) refers to the reconstruc-

tion algorithm of the event: (1) line fit used as first guess for likelihood fit; (2) maximum likelihood

method for muon track; (3) hit probability reconstruction based on radial distribution of OMs

that detect photons; (4) maximum likelihood method assuming cascade event; (5) iterative applica-

tion of maximum likelihood for muon track. Direct hits are photons that arrive within (b)

[

15, +25] ns or (c) [

15, +75] ns of the unscattered time of flight between track and optical mod-

ule. The reduced likelihood parameter

log

divided by the number of degrees of freedom,

where

is the maximized probability. Passing efficiencies (

) relative to the prior stage are shown

at each stage for experimental data, simulated background, and simulated signal. Rejection

factors (

) for experimental data and simulated background are shown for each stage in the two

columns farthest to the right.

1046 AHRENS ET AL. Vol. 583

this analysis, the relative agreement between the measured

and predicted event rates is 30%, which is consistent with

uncertainties in the measured flux of cosmic-ray primaries,

theoretical uncertainty in the interaction models, and sys-

tematic uncertainties in the modeling of the detector

response. However, because of the steeply falling energy

spectrum for atmospheric neutrinos, the mean energy of the

muons induced by charged-current interactions is close to

the energy threshold of the detector, which implies that they

cannot be used to reliably probe the high-energy response of

AMANDA-B10.

6. POINTING RESOLUTION AND

POINT-SOURCE SEARCH

The final stage of the data analysis procedure yields a

sample of 815 events (as is evident from Fig. 7, atmospheric

neutrinos contribute about 25% of the events to the simu-

lated background). Visual inspection of the distribution in

the sky of the final event sample, shown in Figure 8, reveals

no obvious clustering. The increase in event density near the

horizon (decl

) is due to the zenith dependence of the

atmospheric muon component of the background. In order

to perform a quantitative search for possible sources of

high-energy neutrinos in the northern hemisphere, the sky

was divided into nonoverlapping angular bins of approxi-

mately equal solid-angle coverage. A point source would

then be revealed by a statistically significant clustering of

events within a particular angular bin. The optimal bin size

and shape depend on the space-angle resolution of the

detector, which can be expressed in terms of a point-spread

function. The space-angle deviation

between the true

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

5 1015 20253035

data

signal

background

(5)

dir(c)

Normalized Units

Efficiency

(5)

dir(c)

0.2

0.4

0.6

0.8

1.2

5 1015 20253035

Fig.

—

Top

: Similar to Fig. 5, but for analysis stage 13, which involves

the number of direct hits in a time window of

15 to +75 ns.

Bottom

Passing efficiencies—defined as integrated sums, from given value to

infinity, of distributions shown in the top panel—as a function of cut value.

The vertical lines indicate the cut applied in the analysis. [

See the electronic

edition of the Journal for a color version of this figure.

]

Analysis Stage

No. of events

1997 AMANDAB10 data

atmospheric muons

atmospheric neutrinos

total background

01 2 3 45 67 89 10 11 12 13

Fig.

—Number of events remaining in the sample as the selection

criteria in the 13 analysis stages listed in Table 1 are applied sequentially.

The 1997 AMANDA-B10 data (

circles

) are compared to simulated back-

ground from atmospheric muons generated by cosmic-ray interactions

(

squares

) and from muons induced by atmospheric neutrinos (

asterisks

Also shown is the sum of atmospheric muon and neutrino backgrounds

(

triangles

). No normalization was applied, but systematic uncertainty at the

trigger level (analysis stage 0) may be as large as

30%. [

See the electronic

edition of the Journal for a color version of this figure.

]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30

data

signal

background

(5)

down

Normalized Units

Efficiency

(5)

down

0.2

0.4

0.6

0.8

1.2

0 5 10 15 20 25 30

Fig.

—

Top

: Equally normalized distributions for experimental data

(

circles

) and simulated background (

asterisks

) and signal (

triangles

) for

stage 4 of the point-source analysis, which compares the best likelihood for

an upgoing track hypothesis with the likelihood for a track in the opposite

(i.e., downgoing) direction.

Bottom

: Passing efficiencies as a function of cut

value. The efficiency is obtained from the integrated sums of distributions

shown in the top panel from given value to infinity. The vertical lines

indicate the cut applied in the analysis. [

See the electronic edition of the Jour-

nal for a color version of this figure.

]

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1047

angular coordinates of a muon (

true

;

true

) and the recon-

structed coordinates (

rec

;

rec

) is given by

cos

rec

cos

true

sin

rec

sin

true

cos

rec

true

Figure 9 shows the distribution of

and the corresponding

point-spread function, computed from the

-distribution

by dividing by the appropriate solid angle, for the simulated

sample of upward-traveling muons generated by neutrinos

with an

energy spectrum. A median value of

averaged over positive declinations, is achieved. A function

involving the sum of two Gaussian distributions was fitted

to the point-spread function. It yields an amplitude ratio of

25, indicating the importance of the second com-

ponent related to the degrading angular resolution at large

muon energies (Young 2001). Given this point-spread func-

tion and the relatively small number of background events

shown in Figure 8, the optimal slice in zenith angle is 11

(Young 2001). For azimuth angle, a weak optimum occurs

for a width of 12

for the declination band closest to the

horizon. These angular dimensions of the bins were chosen

to maximize the signal to noise.

Two studies were performed to check the predicted space-

angle resolution and absolute pointing accuracy. The first

uses AMANDA events that were also tagged by the GASP

air Cerenkov telescope (Barbagli et al. 1993). GASP deter-

mines the direction of the air shower, and AMANDA meas-

ures the direction of the penetrating muon component. At

AMANDA depths, these events are almost entirely single

muons. Unfortunately, the duty cycle of operation is low, so

the sample size is relatively small. To improve the statistical

accuracy of the angular resolution studies, a second method

based on extensive air showers was developed. This method

utilized events that triggered both the SPASE array and

AMANDA (X. Bai et al. 2003, in preparation). SPASE

responds to the electron and photon content of the shower

front that reaches the surface. Since the direction of muons

within the air shower event is nearly perpendicular to the

shower front, the difference between the direction of the air

shower and the reconstructed muon direction can be used to

deduce the angular resolution of AMANDA. SPASE meas-

ures the direction of an air shower with a pointing resolution

of approximately 1

–2

(Dickinson et al. 2000; depending

on shower size), which is small enough to calibrate the

AMANDA pointing resolution.

In this study, AMANDA data were analyzed using the

procedure outlined in Table 1, with the exception that

angle-dependent cuts were inverted to account for the

downgoing direction of travel of SPASE/AMANDA coin-

cidence events (e.g., the cut at stage 3 was changed to

cos

1). The absolute pointing accuracy is character-

ized by the average of

, the difference between the true

and the reconstructed zenith angle. Because of the excellent

zenith-angle resolution of SPASE, SPASE/AMANDA

coincidence data were used to deduce

using the

reconstructed zenith angles of both detectors,

AMANDA

SPASE

. Figure 10 shows the measured zenith-

angle resolution using SPASE/AMANDA coincidence

events, together with the resolution obtained for a SPASE/

AMANDA simulation of air showers initiated by protons

and iron nuclei. Iron primaries produce a larger fraction of

coincidence events with more than one muon penetrating to

AMANDA depths, which accounts for the small difference

between protons and iron nuclei. The coincidence data sup-

port the predicted angular resolution and show that the

angular offset is small compared to the angular dimensions

of the sky bins. These conclusions are nearly independent of

the choice of cosmic-ray primary.

Also shown in Figure 10 is the expected angular resolu-

tion as function of declination for single muons with ener-

gies of 0.1 and 4 TeV within the detector volume. These

muon energies were chosen to be representative of the aver-

age muon energy that were initiated by atmospheric neutri-

nos and by a source with a differential energy spectrum

proportional to

. The predicted value for the absolute

offset is less than 1

5, which is consistent with results

obtained by additional study of the SPASE/AMANDA

Mkn 501

Mkn 421

NGC4151

1ES2344

3C66A

1ES1959+650

Crab Nebula

Cassiopeia A

Cygnus X3

Geminga

Fig.

—Sky plot of 815 events obtained from the point-source analysis.

Horizontal coordinates are right ascension, and vertical coordinates are

declination. Also shown are the sky coordinates for 10 potential high-

energy neutrino sources. [

See the electronic edition of the Journal for a color

version of this figure.

]

0.05

0.1

0.15

0.2

0.25

0 2468 10 12 14 16 18 20

mean

RMS

median

= 5.00

= 3.82

= 3.94

[degrees]

Arbitrary Units

[degrees]

Point spread function

= 0.33

= 1.90

= 0.08

= 4.45

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2468 10 12 14 16 18 20

Fig.

—

Top

: Distribution of space angle

between true and recon-

structed muon track direction for simulated signal with neutrino energy

spectrum proportional to

, averaged over direction.

Bottom

: Point-

spread function for signal in AMANDA-B10, deduced from the space-

angle distribution in the top panel. A function composed of the sum of two

Gaussians was used to characterize this distribution.

1048 AHRENS ET AL. Vol. 583

and GASP/AMANDA coincidence events (Rawlins 2001;

X. Bai et al. 2003, in preparation).

The offset is due to bias

in the AMANDA event reconstruction, which tends to pro-

duce more vertical events. This effect is most evident from

the high-energy muon simulation, which shows that the

angular offset changes sign for positive and negative decli-

nations. Since the absolute offset is substantially smaller

than the angular resolution and small compared to the size

of the search bin, the offset has minimal impact on the signal

efficiency. For a zenith (declination) offset of 1

5, 6% of the

signal events are shifted to the neighboring bin. The bottom

panel of the figure also shows that the angular resolution for

upward-traveling events is slightly better than for events

traveling in the downward direction, presumably because of

the asymmetry in the response of the photomultiplier tubes,

which are oriented toward the center of the Earth.

To obtain approximately equal solid-angle coverage for

all bins, the northern sky is divided into 154 nonoverlapping

bins, using the calculated optimal declination slice (11

25)

and a varying number of bins in azimuth for the resulting

eight declination bands—from 30 near the horizon to three

near +90

declination. Each angular bin is then tested for

an excess of events by computing the significance,

¼?

log

;

where

is the probability of the bin containing at least the

observed number of events

, assuming that fluctuations

are described by a Poisson distribution. The expected

mean number of events

is obtained by taking the aver-

age of the number of events in all other bins in the same

declination slice. The polar location of AMANDA

assures equal sky coverage for all declinations, independ-

ent of time gaps in the collection of data. Figure 11

shows the distribution of significance for the experimental

data and for random fluctuation of the background

events. This noise estimate is obtained by randomizing

the right ascension coordinate of the data events, then

recalculating

for each bin. A point-source candidate is

identified by a large observed value of significance with a

large ratio to the significance expected from random fluc-

tuations of background. To avoid the statistical problem

of a potential source near a bin boundary distributing

signal between two adjacent bins, the procedure was

repeated with the grid shifted by one-half of a bin in

both declination and azimuth. The largest value of signif-

icance,

85, appears in the bottom panel. Taking

into account the 154 bins in the sky and the two versions

of the sky grid, there is a 40% probability that the most

significant sky bin is produced by random fluctuation of

background. Therefore, the distribution of significance

shows no evidence of a source.

Another approach was also investigated, using the angu-

lar correlation function between event pairs to avoid the

problem of a source near a bin boundary, but this alternate

approach did not reveal sources either (Young 2001).

Available at http://area51.berkeley.edu/manuscripts/

20011002xx-kaths_thesis.pdf.

80 60 40 20 0 20 40 60 80

signal (

= 4 TeV)

signal (

= 100 GeV)

SPASE/AMANDA coincidence data

proton simulation

iron simulation

Declination [degrees]

Δθ

[degrees]

Declination [degrees]

median

[degrees]

80 60 40 20 0 20 40 60 80

Fig.

10.

—Offset in reconstructed zenith angle (

top

) and median space

angle (

bottom

) as a function of declination. Positive declination

corresponds to upward-traveling events in the AMANDA array. SPASE/

AMANDA coincidence data (

squares

) are compared to expectation assum-

ing that the cosmic-ray elemental composition is entirely protons (

circles

)

or iron nuclei (

triangles

). Also shown is the expectation for signal (i.e.,

neutrino-induced muons) with two different energies within the detector.

[

See the electronic edition of the Journal for a color version of this figure.

]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Significance (

)

No. of bins

data

background

nominal grid

shifted grid

Significance (

)

No. of bins

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Fig.

11.

—Distribution of significance for the 154 sky bins. Data

(

squares

) are compared to expectation from randomized background

(

circles

). The statistical uncertainty of the randomized background is negli-

gible. The top panel shows the results for the nominal sky grid. The sky grid

used in the bottom panel has been shifted from the nominal sky grid by

one-half of a bin in both right ascension and declination. [

See the electronic

edition of the Journal for a color version of this figure.

]

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1049

7. FLUX LIMITS

The absence of a detected source translates into an upper

limit on the high-energy neutrino flux. Neutrino flux and

neutrino-induced muon flux limits depend on the effective

area of the detector

eff

for a muon with energy

. The

effective area, obtained by dividing the signal rate by the

incident flux, is determined from simulations by

eff

Þ¼

GEN

;

where

GEN

is the cross-sectional area of the cylinder in the

simulation that contains all neutrino interaction vertices

and

is the fraction of generated muon events that survive

the 13-stage data analysis procedure. As an example, results

are shown in Figure 12 for muon vertices located near the

detector. The effective area is computed as a function of

declination for muons with energies of 1, 10, and 100 TeV.

These effective areas can be contrasted to the geometric

cross section of the instrumented volume of deep ice, which

spans from 1

in the vertical direction to

in the horizontal direction.

The

average

effective area, folding in the source spectra,

detector response, and the probability of a neutrino-nucleon

interaction, is given by

eff

ice

GEN

max

min

;

min

Þi

max

min

;

where the index

denotes either

,and

min

10 GeV

and

max

GeV define the energy range in the simula-

tion, which safely brackets the interval of interest for most

theoretical models. The other variables are

, Avogadro’s

number,

ice

, the molar density of nucleons in ice, and

the charged-current cross section for

(or

) interactions.

The term

accounts for neutrino absorption in the

Earth, and

;

min

Þi

is the average propagation length

for a muon created by a neutrino with energy

, corrected

for the energy threshold of the detector. In this calculation,

the neutrino interaction vertices are located randomly

within a volume that is large compared to the instrumented

volume of the detector. The propagation programs properly

account for muon energy losses.

The muon differential flux is related to the neutrino differ-

ential flux by

Þh

;

min

Þi

The energy-averaged muon effective area is presented in

Figure 13 for different spectral indexes. The energy response

of AMANDA is described by the distribution of

at the

detector, which depends on the spectral index of the neu-

trino spectrum. Figure 14 shows the distribution for differ-

ential spectra proportional to

and

. For

, the

most probable muon energy (mode) is 5 TeV, and the cen-

tral 90% of the muon events are within the energy interval

80 GeV to 200 TeV. For a spectral index of 3, appropriate

for atmospheric neutrinos, the most probable detected

energy of the muon is much lower.

If neutrino emission from a point source is described by a

differential energy spectrum, the energy-averaged flux limit

is calculated from

limit

;

bgr

live

bin

eff

Declination [degrees]

eff

]

= 100 TeV

= 10 TeV

= 1 TeV

10000

20000

30000

40000

50000

0 102030405060708090

Fig.

12.

—AMANDA-B10 effective area for muon detection as a func-

tion of declination (90

is vertically up) for three different muon energies at

the detector. The vertical error bars are statistical. [

See the electronic edition

of the Journal for a color version of this figure.

]

2.3

2.5

2.7

Input spectrum:

Declination [degrees]

–

eff

]

2000

4000

6000

8000

10000

12000

0 102030 40506070 8090

Fig.

13.

—AMANDA-B10 average effective area for muon detection as

a function of declination (90

is vertically up) for assumed differential

neutrino spectral indexes between 2 and 3. The vertical error bars indicate

the uncertainty obtained from studies described in

8. [

See the electronic

edition of the Journal for a color version of this figure.

]

1050 AHRENS ET AL. Vol. 583

The quantity

;

bgr

is the upper limit on the number

of signal events at the 90% confidence level, calculated fol-

lowing the unified procedure of Feldman & Cousins (1998),

where

is the observed number of events in a potential

source bin and

bgr

is the expected number of background

events. For the binning technique employed in our point-

source search,

bgr

is determined by averaging the number

of observed events over the declination band, excluding the

bin being considered. The efficiency factor

bin

accounts for

the finite angular resolution and the possible noncentral

location within the bin of a potential source. The factor

live

is the operational live time of the detector. The resulting

muon and neutrino flux limits are shown in Figures 15 and

16, respectively, for various assumed spectral indexes

between 2 and 3.

Figure 17 shows a comparison of the AMANDA flux lim-

its with a representative sample of neutrino detectors

located in the Northern Hemisphere. The AMANDA-B10

detector approaches its maximum sensitivity for declina-

tions greater than +30

, which complements the sky regions

covered by neutrino detectors such as MACRO (Montaruli

et al. 1999; Ambrosio et al. 2001; Perrone et al. 2001) and

Super-Kamiokande (Matsuno et al. 2001).

With only

130.1 days of detector live time, the muon flux limits for pos-

itive declinations approach those achieved for the southern

sky. The AMANDA flux limits were calculated for

GeV, while both Super-Kamiokande and MACRO present

fluxes for

1–2 GeV, but for relatively hard differential

neutrino spectra, such as

, the impact of energy thresh-

old on muon flux limits is modest (Biron 2002).

In addition to the general search for a point source, a

number of potential sources of particular interest were

investigated by performing the significance test while cen-

tering the search bin on their sky coordinates. The result-

ing flux limits are presented in Table 2. As one

interesting example, we compare the AMANDA limit on

log

/GeV)

Normalized Units

input spectrum

mode

= 5 TeV

mode

= 80 GeV

0.02

0.04

0.06

0.08

0.1

0.12

12 345 67

Fig.

14.

—Neutrino-induced muon energy distribution at the detector.

The differential neutrino spectra used as input for the simulation are pro-

portional to

(

solid curve

) and

(

dashed curve

), respectively. The

most probable energy for each distribution is shown.

input spectrum

2.3

input spectrum

2.5

input spectrum

2.7

input spectrum

Declination [degrees]

limit

[cm

]

0 102030 405060 708090

Fig.

15.

—Neutrino flux limit (90% CL) for various spectral indexes. The

results are shown as a function of declination, averaged over right

ascension. Power-law exponent refers to the differential neutrino energy

spectrum. The vertical error bars indicate the uncertainty obtained from

systematic studies [

See the electronic edition of the Journal for a color version

of this figure.

]

input spectrum

2.3

input spectrum

2.5

input spectrum

2.7

input spectrum

Declination [degrees]

limit

[cm

]

0 102030 405060 708090

Fig.

16.

—Neutrino-induced muon flux limit (90% CL) for various

spectral indexes. The results are shown as a function of declination, aver-

aged over right ascension. Note that the power-law exponent refers to the

differential neutrino energy spectrum. [

See the electronic edition of the Jour-

nal for a color version of this figure.

]

Available at http://www.copernicus.org/icrc/papers/ici7384_p.pdf.

Available at http://area51.berkeley.edu/manuscripts.

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1051

the neutrino flux from Mrk 501 to the observed gamma-

ray flux and this flux corrected for intergalactic absorp-

tion by infrared photons in Figure 18. Assuming that the

neutrino energy spectrum is proportional to the inferred

gamma-ray spectrum at the source, the AMANDA limit

constrains the proportionality factor. For example, the

ratio of the flux of neutrinos to the flux of gamma rays

must be less than 10 if the source spectrum of Konopelko

et al. (1999) is assumed. Recent work (de Jager & Stecker

2002) suggests that the ratio may be smaller.

8. IMPACT OF SYSTEMATIC UNCERTAINTIES

ON FLUX LIMITS

In the absence of a well-understood source of high-energy

neutrinos, the sensitivity of the AMANDA-B10 detector, as

expressed in terms of the effective area and angular resolu-

tion, had to be estimated from detector simulations. The

required input relies on knowledge of detector performance

extracted from, e.g., laboratory measurements of the indi-

vidual components, in situ measurements of the optical

Fig.

17.

—Upper limit on the muon flux (90% CL) as a function of decli-

nation. The solid curve is the AMANDA-B10 limit, averaged over right

ascension, and the region delineated by the long-dashed curves provides a

guide to the statistical fluctuation within the declination interval (see Table

4). The band defined by the short-dashed curves indicates the range of limits

presented by MACRO (Montaruli et al. 1999; Ambrosio et al. 2001;

Perrone et al. 2001) and Super-Kamiokande (Matsuno et al. 2001). [

See the

electronic edition of the Journal for a color version of this figure.

]

TABLE 2

Muon and Neutrino Flux Limits on Selected Point Sources

Source Model

bgr

(TeV)

limit

(10

)

limit

(10

)

Mrk 501 ....................... 1 7 3.5 0.3–20 86.0 38.9

Mrk 501 ....................... 2 7 3.5 1–1000 9.5 14.6

Mrk 421 ....................... 3 4 3.7 1–1000 11.2 9.7

NGC 4151.................... 3 5 3.6 1–1000 12.9 10.9

NGC 4151.................... 4 5 3.6 60–2500 0.0042 5.6

1ES 2344...................... 5 5 2.9 1–400 12.5 10.3

3C 66A......................... 5 3 3.5 0.8–250 7.2 6.6

1ES 1959+650.............. 5 4 1.7 0.8–250 13.2 9.7

Crab Nebula ................ 5 2 5.6 1–1000 4.2 5.0

Cas A........................... 5 3 2.2 1.8–1000 9.8 7.6

Cyg X-3 ....................... 5 2 3.4 1–1000 4.9 4.6

Geminga ...................... 5 4 7.1 1.8–1000 6.8 9.1

Notes.

—Muon and neutrino flux limits on selected sources for

10 GeV. The term

is the number

of observed events in the search bin, and

bgr

is the expected background. The energy interval

contains

90% of the neutrino events, and the flux limits are corrected for systematic uncertainty (see

8). Representa-

tive survey of models (second column): (1) neutrino spectrum identical to measured photon spectrum

(Aharonian et al. 1999); (2)

; (3) Szabo & Protheroe 1992; (4) Stecker et al. 1991; (5)

log

(

/ TeV)

log

(

/ TeV m

)

Markarian 501,

= 0.0336

AMANDA flux limit

observed gamma flux (HEGRA)

corrected gamma flux (Konopelko, et al.)

1 0.5 0 0.5 1 1.5 2

Fig.

18.

—Time-averaged spectrum of gamma rays from Mrk 501

observed in 1997 (Aharonian et al. 1999; Krennrich et al. 1999) and cor-

rected for intergalactic absorption by the diffuse infrared background

(Konopelko et al. 1999). Gamma-ray flux is compared to the AMANDA

neutrino limit assuming an energy dependence on the neutrino flux

proportional to

See the electronic edition of the Journal for a color

version of this figure.

]

1052 AHRENS ET AL. Vol. 583

properties of the ice, and calibration studies. Consequently,

the predicted sensitivity is affected by uncertainty in this

information. Table 3 lists the dominant contributions to

systematic uncertainties. The uncertainty in the right

column is defined as the variation

jð

eff

nom

eff

nom

eff

Þj

of the effective area from its value determined

with the nominal set of input parameters,

nom

eff

, given by the

area,

eff

, obtained by varying the specified parameter

(index

) by its estimated uncertainty.

The most significant component is generated from the

uncertainty in the angular dependence of the OM sensitiv-

ity. It arises mainly from a lack of detailed understanding of

the physics governing the refreezing process in the water col-

umn required to be melted for the deployment of OMs. A

local increase in scattering from air bubbles trapped in the

vicinity of the OM translates into a modulation of its angle-

dependent acceptance. This effect is difficult to disentangle

from the intrinsic angular dependence of the OM sensitivity,

which was measured in the laboratory. An event sample

highly enriched in atmospheric muons was used to investi-

gate the in situ angle dependence of the OM sensitivity

(Ahrens et al. 2002a). The modification to the angular sensi-

tivity leads to a 25% uncertainty in the effective area.

Since the angle-integrated sensitivity of the OM is a

poorly constrained parameter in this analysis, we also inves-

tigated the impact of varying the absolute sensitivity of the

OM. It was parameterized by a wavelength-dependent func-

tion that included the PMT quantum efficiency, the OM col-

lection efficiency, obscuration by nearby cables, and

absorption properties of the glass pressure vessel and cou-

pling gel. We obtain a fractional uncertainty of 0.15 in the

effective area after reducing the absolute OM sensitivity by

15%, a value consistent with the atmospheric neutrino

results. Further reduction is inconsistent with observed

experimental trigger rates.

As mentioned in

4, two muon propagation routines

were employed to show that systematic variations in the

effective area for signal (i.e., upward-traveling) muons

were between 5% and 10%. This is much less than

observed for studies of atmospheric muons, presumably

because of the much weaker angular dependence of the

average path length. Possible uncertainties in timing and

position calibration of individual OMs are included by

varying these parameters to the largest extent allowed by

the imprecision of the calibration procedures. The effec-

tive area changes by 10%. A conservative estimate of the

variation in sensitivity introduced by uncertainties in the

depth-dependent optical properties and their approximate

treatment in the detector simulation is obtained by sub-

stituting the nominal bulk ice model, containing a param-

eterization of the measured dust strata, with a

homogeneous ice model. The impact on effective area is

less than 15%.

The impact of the most dominant systematic uncertain-

ties on the average effective area is shown in Figure 19,

where the systematic variations have been applied one at a

time, with the exception of the muon propagation curve,

which also includes the variation of the angular OM

sensitivity.

The variation of the detector sensitivity due to systematic

uncertainties was studied by adjusting the physical parame-

ters in the detector simulation. The parameters were

adjusted according to the known or estimated uncertainties

listed in Table 3, which are assumed to bound the true val-

ues of the parameters. Systematic uncertainty was included

according to the prescription of Conrad et al. (2003), which

is an extension of the method of Cousins & Highland

(1992). The calculations assumed that the distribution of

systematic uncertainty was flat and bounded by the maxi-

mum and minimum values for a given declination bin,

found in Figures 20 and 21.

The solid curves in Figures 20 and 21 indicate the flux lim-

its after adjusting for systematic uncertainty. They are valid

for declination greater than +5

. The limits including sys-

tematic uncertainties are about 25% worse than those

obtained from the simulation with nominal input parame-

ters. Finally, the flux limits change by less than 6% because

of the effects of zenith offset and the variation in

median

due

to declination (Young 2001). These small effects were not

taken into consideration in the limit calculations.

9. DISCUSSION

The previous sections have shown that AMANDA-B10

has unprecedented sensitivity to high-energy neutrinos and

possesses the necessary angular response and background

TABLE 3

Systematic Uncertainty in AMANDAB10 Effective Area

Source of Systematic Uncertainty

Error in

eff

(%)

Angular dependence of OM sensitivity............................

Absolute OM sensitivity..................................................

Muon propagation..........................................................

Calibration (timing and geometry)..................................

Hardware simplifications in detector simulation .............

Optical properties of bulk ice ..........................................

Declination [degrees]

–

eff

]

nominal (layered ice)

homogeneous ice

absolute OM sensitivity

angular OM sensitivity

muon propagation

2000

4000

6000

8000

10000

12000

0 102030405060708090

Fig.

19.

—Comparison of average muon effective area for differential

neutrino signal proportional to

. See text for explanation of legend.

Statistical uncertainty is indicated by vertical lines, unless it is obscured by

the symbol. [

See the electronic edition of the Journal for a color version of this

figure.

]

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1053

rejection to search for point emission of these particles from

astronomical objects; i.e., it is a novel telescope that detects

the neutrino messenger. The sensitivity and angular

response were determined by simulation. The reliability of

these programs was established by utilizing the known sig-

nals generated by (downgoing) atmospheric muons and

(upgoing) atmospheric neutrinos. The angular response was

confirmed by the study of air shower events that triggered

both AMANDA-B10 and SPASE. Systematic uncertainty

in the analysis procedure was also addressed.

The search for point sources of high-energy neutrinos

revealed no candidates. A set of event selection criteria was

determined by optimizing the signal-to-noise ratio for a sig-

nal with a hard energy spectrum, yet this analysis retains

reasonable sensitivity for softer spectra. The upper limits on

muon flux for all search bins in the northern hemisphere are

presented in Table 4.

The neutrino flux limits in Figure 15 are inferred from the

assumption of a power-law energy spectrum. This proce-

dure is reliable if the mean energy of the neutrino-induced

muon is compatible with the energy response of the detec-

tor. For example, Figure 14 shows that

at the detector

brackets the interval between 0.1 and 10

TeV for source

spectra proportional to

. Two lines of evidence show

that the simulated energy response of the detector is valid

over this interval. First, the agreement between the detected

and expected rates of atmospheric neutrinos shows that the

response of AMANDA is being correctly modeled in the

sub-TeV region. Second, the tails of the

-distribution are

sensitive to brighter events within AMANDA, which

are roughly equivalent to single muons with energy above 1

TeV. We know of no reason to doubt the predicted energy

response for

TeV. Evaluation and calibration of

the energy response beyond 10

TeV remain an ongoing

activity.

Not all model predictions are well characterized by

power-law energy spectra. Therefore, Table 2 shows the

results for a selection of models in the literature. The

inferred limits on neutrino flux apply to point sources with

continuous emission (or episodic emission averaged over

the time interval of data collection) and power-law energy

spectra with a fixed spectral index. The limits presented here

for sources at large positive declination complement exist-

ing data, so that comparable limits now exist for the entire

sky.

During 1997, the TeV gamma-ray emission of two

nearby AGN blazars (Mrk 421 and 501) were observed

to exhibit episodic flaring. If neutrino emission follows

the same time variability, then it may be possible to

improve the signal-to-noise ratio by eliminating the peri-

ods of relatively low output. Multiple detections of Mrk

501 from several air Cerenkov instruments allowed nearly

continuous monitoring, including periods when the Moon

was shining. However, monitoring by multiple instru-

ments extended only from March to late August. Because

of uncertainties in the details of the time dependence of

the gamma-ray emission,

neutrino

flux limits are not

greatly improved by restricting the analysis to high-flux

periods of gamma-ray emission.

While this paper describes an analysis dedicated to the

search for point sources, another strategy was developed

based on the event selection of the atmospheric neutrino

analysis (Biron 2002). The results of this complementary

analysis are consistent with the results presented here. The

absolute efficiency was extracted by comparing to the known

flux from atmospheric neutrinos. Moreover, the second

analysis was subject to different systematic uncertainties.

The method based on the atmospheric neutrino analysis

retained a smaller event sample of 369 events, of which

270 are expected from atmospheric neutrinos. The cut

selections produce an implicit optimization on more vertical

Declination [degrees]

limit

[cm

]

nominal (layered ice)

homogeneous ice

absolute OM sensitivity

angular OM sensitivity

muon propagation

corrected

0 10 2030 405060 7080 90

Fig.

20.

—Comparison of muon flux calculations for differential neutrino

signal proportional to

. See text for explanation of legend. Statistical

uncertainty is small and not shown. The solid curve (corrected) includes

systematic uncertainty and indicates the final result of this work. [

See the

electronic edition of the Journal for a color version of this figure.

]

Declination [degrees]

limit

[cm

]

nominal (layered ice)

homogeneous ice

absolute OM sensitivity

angular OM sensitivity

muon propagation

corrected

0 10 2030 405060 7080 90

Fig.

21.

—Comparison of neutrino flux calculations for differential

neutrino signal proportional to

. See text for explanation of legend.

Statistical uncertainty is small and not shown. The solid curve (corrected)

includes systematic uncertainty and indicates the final result of this work.

[

See the electronic edition of the Journal for a color version of this figure.

]

1054 AHRENS ET AL. Vol. 583

events and/or softer energy spectra. Figure 22 compares the

average effective area of the two analyses for an assumed

differential spectra proportional to

. The best flux limits

for soft spectra are obtained by atmospheric neutrino analy-

sis, but the neutrino and muon flux limits for either analysis

are much larger than obtained for an assumed power law of

an index of

2.0.

While the flux limits for any particular source or direction

in the northern hemisphere can be extracted from this analy-

sis (see Table 4), flux limits, both integral and pseudodiffer-

ential, for a preselected list of 62 sources have been reported

(Biron 2002). These include all known TeV gamma-ray

blazars, nearby QSOs, and Galactic TeV gamma-ray

sources in the northern hemisphere. The list also includes

TABLE 4

Muon Flux Limits

Decl.

(deg)

R.A.

(hours)

limit

(10

)

Decl.

(deg)

R.A.

(hours)

limit

(10

)

Decl.

(deg)

R.A.

(hours)

limit

(10

)

85........... 4.0 2.5 39........... 7.8 6.1 17........... 7.9 9.0

12.0 6.5 8.9 2,5 8.7 9.0

20.0 10.5 9.9 15.5 9.5 19.9

73........... 1.3 6.9 11.0 13.5 10.3 14.9

4.0 4.2 12.0 13.5 11.2 42.6

6.7 2.1 13.0 8.0 12.0 11.9

9.3 6.9 14.1 8.0 12.8 34.1

12.0 13.7 15.1 8.0 13.7 24.6

14.7 6.9 16.2 10.6 14.5 42.6

17.3 9.6 17.2 15.5 15.3 8.9

20.0 4.2 18.3 3.9 16.1 11.9

22.7 4.2 19.3 6.1 17.0 14.9

62........... 0.9 7.9 20.3 10.6 17.8 8.9

2.6 5.5 21.4 3.9 18.6 42.6

4.3 12.1 22.4 3.9 19.4 19.9

6.0 3.4 23.5 6.1 20.3 19.9

7.7 7.9 28........... 0.4 20.5 21.1 48.0

9.4 5.5 1.3 20.5 21.9 14.9

11.1 7.9 2.2 7.1 22.8 34.1

12.9 1.9 3.1 13.9 23.6 29.1

14.6 5.5 4.0 24.0 6............. 0.4 33.6

16.3 3.5 4.9 13.9 1.2 64.9

18.0 3.5 5.8 7.1 2.0 127.2

19.7 7.9 6.7 20.5 2.8 64.9

21.4 7.9 7.6 13.9 3.6 47.8

23.1 9.9 8.4 20.5 4.4 33.6

51........... 0.6 7.7 9.3 7.1 5.2 96.1

1.9 10.0 10.2 24.0 6.0 64.9

3.2 2.2 11.1 20.5 6.8 78.0

4.4 7.7 12.0 24.0 7.6 78.0

5.7 5.9 12.9 5.4 8.4 47.8

6.9 10.0 13.8 13.9 9.2 64.9

8.2 2.2 14.7 5.4 10.0 64.9

9.5 10.0 15.6 20.5 10.8 127.2

10.7 5.9 16.4 16.7 11.6 47.9

12.0 1.6 17.3 5.4 12.4 33.6

13.3 10.0 18.2 16.7 13.2 143.5

14.5 5.9 19.1 7.1 14.0 24.9

15.8 10.0 20.0 10.2 14.8 47.8

17.1 7.7 20.9 7.1 15.6 33.6

18.3 14.1 21.8 13.9 16.4 64.9

19.6 3.9 22.7 10.2 17.2 47.8

20.8 5.9 23.6 7.1 18.0 47.8

22.1 12.4 17........... 0.4 48.0 18.8 112.4

23.4 7.7 1.2 34.1 19.6 96.1

39........... 0.5 10.6 2.1 14.9 20.4 33.6

1.6 15.5 2.9 51.9 21.2 96.1

2.6 8.0 3.7 19.9 22.0 24.9

3.7 13.5 4.6 24.6 22.8 64.9

4.7 3.9 5.4 14.9 23.6 78.0

5.7 15.5 6.2 4.5

6.8 6.1 7.0 9.0

Notes.

—Neutrino-induced muon flux upper limits for source spectra proportional to

. The impact of systematic uncertainty is included. Angu-

lar coordinates refer to the center of the search bin.

No. 2, 2003 SEARCH FOR HIGH-ENERGY NEUTRINO SOURCES 1055

microquasars, the five most luminous AGNs in wavelength

bands that span across MeV, X-ray, infrared, and radio

bands. Of particular interest are radio galaxies with strong

emission at GHz frequencies. We have also investigated BL

Lac objects that are close to the arrival directions of the very

highest energy cosmic rays (Tinyakov & Tkachev 2001) and

the 10 reported cosmic-ray doublets at extreme energies

(Uchihori et al. 2000).

10. FUTURE

The technique employed in this paper optimized the selec-

tion criteria on signal to noise. Because of the relatively

large number of sky bins and the relatively low number of

events in any individual bin, the analysis procedure pro-

duced event samples that are dominated by poorly recon-

structed atmospheric muons rather than upward-traveling

atmospheric neutrino background. However, as the back-

ground rejection of downgoing events improves with

larger detectors, such as AMANDA-II, this trend may not

continue.

AMANDA-II, completed in 2000 January, surrounds the

B10 core with nine additional strings, more than doubling

the number of optical modules. For this broader configura-

tion, the effective area for neutrino-induced muons remains

relatively constant over the entire hemisphere (Barwick et

al. 2001).

Consequently, AMANDA-II is expected to

achieve a factor of 5 improvement in sensitivity for nearly

horizontal events compared to AMANDA-B10 (Wischnew-

ski et al. 2001).

The greater statistical sample of atmo-

spheric neutrinos will allow better tests of the detector

simulation programs, especially near the horizon. With the

data already collected on tape, AMANDA-II can observe

(or exclude) neutrino fluxes that are approximately 1 order

of magnitude below the limits presented here, as shown in

Figure 1.

This research was supported by the following agencies:

the US National Science Foundation Office of Polar Pro-

grams and Physics Division; the University of Wisconsin

Alumni Research Foundation; the US Department of

Energy; the Swedish Natural Science Research Council; the

Swedish Polar Research Secretariat; the Knut and Alice

Wallenberg Foundation, Sweden; the German Ministry for

Education and Research; the US National Energy Research

Scientific Computing Center (supported by the Office of

Energy Research of the US Department of Energy); the

University of California, Irvine, AENEAS Supercomputer

Facility; and the Deutsche Forschungsgemeinschaft

(DFG). C. Pe

rez de los Heros received support from the EU

fourth framework of Training and Mobility of Researchers,

and D. F. Cowen acknowledges the support of the NSF

CAREER program. P. Desiati was supported by the

Koerber Foundation.

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Available at http://area51.berkeley.edu/manuscripts/

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