doi:10.1016/j.nima.2003.12.007

Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

Calibration and survey of AMANDA with the

SPASE detectors

J. Ahrens

, X. Bai

b,1

, S.W. Barwick

, R.C. Bay

, T. Becka

, K.-H. Becker

E. Bernardini

, D. Bertrand

, F. Binon

, A. Biron

,S.B

oser

, O. Botner

A. Bouchta

f,2

, O. Bouhali

, T. Burgess

, S. Carius

, T. Castermans

, D. Chirkin

J. Conrad

, J. Cooley

, D.F. Cowen

, A. Davour

, C. De Clercq

, T. DeYoung

l,3

P. Desiati

, J.-P. Dewulf

, E. Dickinson

o,1

, P. Doksus

, P. Ekstr

, R. Engel

b,4

P.Evenson

b,1

,T.Feser

,T.K.Gaisser

,R.Ganugapati

,M.Gaug

,H.Geenen

L.Gerhardt

,A.Goldschmidt

,A.Hallgren

,F.Halzen

,K.Hanson

,R.Hardtke

T. Hauschildt

, M. Hellwig

, P. Herquet

, G.C. Hill

, J.A. Hinton

o,1

, B. Hughey

P.O. Hulth

, K. Hultqvist

, S. Hundertmark

, J. Jacobsen

, A. Karle

, J. Kim

L. K

opke

, M. Kowalski

, K. Kuehn

, J.I. Lamoureux

, H. Leich

, M. Leuthold

P. Lindahl

, I. Liubarsky

, J. Lloyd-Evans

o,1

, J. Madsen

, K. Mandli

P. Marciniewski

, D. Martello

b,5,1

, H.S. Matis

, C.P. McParland

, T. Messarius

T.C. Miller

b,6,1

, Y. Minaeva

, P. Mio

inovi

, P.C. Mock

c,7

, R. Morse

T. Neunh

offer

, P. Niessen

n,8

, D.R. Nygren

,H.

Ogelman

, Ph. Olbrechts

C. Perez de los Heros

, A.C. Pohl

, R. Porrata

c,9

, P.B. Price

, G.T. Przybylski

K. Rawlins

, E. Resconi

, W. Rhode

, M. Ribordy

, S. Richter

, K. Rochester

o,1

J. Rodr

ıguez Martino

, P. Romenesko

, D. Ross

, H.-G. Sander

, T. Schmidt

K. Schinarakis

, S. Schlenstedt

, D. Schneider

, R. Schwarz

, A. Silvestri

M. Solarz

, G.M. Spiczak

r,1

, C. Spiering

, M. Stamatikos

, T. Stanev

b,1

D. Steele

, P. Steffen

, R.G. Stokstad

, K.-H. Sulanke

, I. Taboada

, S. Tilav

b,1

C. Walck

, W. Wagner

, Y.-R. Wang

, A.A. Watson

o,1

, C. Weinheimer

ARTICLE IN PRESS

*Corresponding author.

E-mail address:

gaisser@bartol.udel.edu (T.K. Gaisser).

SPASE Collaboration.

Present address: CERN, CH-1211 Geneve 23, Switzerland.

Present address: Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064, USA.

Present address: Forschungszentrum Karlsruhe, Institut f

ur Kernphysik, Postfach 3640, 76021 Karlsruhe, Germany.

Present address: Dipt. di Fisica & INFN, Lecce, Italy.

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

Present address: Optical Networks Research, JDS Uniphase, 100 Willowbrook Rd., Freehold, NJ 07728-2879, USA.

Present address: Bartol Research Institute, University of Delaware, Newark, DE 19716, USA.

Present address: L-174, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550, USA.

0168-9002/$ - see front matter

doi:10.1016/j.nima.2003.12.007

C.H.Wiebusch

f,2

,C.Wiedemann

,R.Wischnewski

,H.Wissing

,K.Woschnagg

W. Wu

, G. Yodh

, S. Young

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

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

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

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

Fachbereich 8 Physik, BUGH Wuppertal, D42097 Wuppertal, Germany

DESYZeuthen, D15735 Zeuthen, Germany

Universit

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

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

Department of Physics, Stockholm University, SCFAB, S10691 Stockholm, Sweden

Deptartment of Technology, Kalmar University, S39182 Kalmar, Sweden

Universit

e de MonsHainaut, 19 Avenue Maistriau, Mons 7000, Belgium

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

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

Vrije Universiteit Brussel, Dienst ELEM, B1050 Brussel, Belgium

Univerity of Leeds, Leeds, UK

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Imperial College, London, UK

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

Departamento de F

ısica, Universidad Sim

on Bol

ıvar, Apdo. Postal 89000, Caracas, Venezuela

The SPASE Collaboration and The AMANDA Collaboration

Received 13 March 2003; received in revised form 14 October 2003; accepted 9 December 2003

Abstract

We report on the analysis of air showers observed in coincidence by the Antarctic Muon and Neutrino detector array

(AMANDA-B10) and the South Pole Air Shower Experiment (SPASE-1 and SPASE-2). We discuss the use of

coincident events for calibration and survey of the deep AMANDA detector as well as the response of AMANDA to

muon bundles. This analysis uses data taken during 1997 when both SPASE-1 and SPASE-2 were in operation to

provide a stereo view of AMANDA.

PACS:

96.40.DE; 96.40.Pq; 96.40.Tv

Keywords:

Cosmic rays; Neutrino telescopes

1. Introduction

One of the advantages of a neutrino telescope in

ice is the possibility of an air shower array on the

surface to make coincidence measurements with

the deep detector. The presence of South Pole Air

Shower Experiment (SPASE) on the surface

provides a set of externally tagged muon bundles

that can be measured by Antartic Muon and

Neutrino detector array (AMANDA). Such mea-

surements allow a study of the response of

AMANDA that is complementary to studies of

the deep detector with atmospheric muons and

neutrinos, internal calibration sources and Monte

Carlo simulations. In particular, the surface array

makes possible an independent check of the

angular resolution of the deep detector. In addi-

tion it makes possible a muon survey of AMAN-

DA optical module (OM) locations and ice

properties that complements internal assessments.

Measurements of the muon bundles under

1500 m of ice in coincidence with showers at the

ARTICLE IN PRESS

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

348

surface also allows a novel study of the primary

cosmic-rays in the region of the knee of the

cosmic-ray spectrum. In this paper we describe the

calibration and survey of AMANDA with SPASE.

In the process we study the response of AMAN-

DA to muon bundles. Such measurements form

the basis of the composition study, which is the

subject of a separate paper [1].

1.1. Description of the surface arrays

There were two SPASEs. SPASE-1 [2–4] was an

array of 16 detectors, each 1 m

of scintillator, at

14 locations on a 30 m triangular grid. The array

operated for 10 years from the end of 1987 to the

end of 1997. SPASE-2

[5]

is an array of 120

modules grouped into 30 stations on a 30 m

triangular grid. Each module contains a scintilla-

tor of 0

The enclosed area of SPASE-1 was

approximately 6000 m

while that of SPASE-2 is

16,000 m

. SPASE-2 began full operation at the

beginning of 1996. AMANDA was deployed in

stages; the 10-string array (AMANDA-B10) began

operation in 1997[6]. For the purpose of studying

the response of AMANDA, 1997 is particularly

important because of the unique opportunity to

view AMANDA in stereo, from two different

directions and at two zenith angles (27

for

SPASE-1 and 12

for SPASE-2). In addition, the

GASP air Cherenkov telescope [7] was also

operating the same year and providing tagged

coincidence events. We therefore concentrate in

this paper on coincident data collected in 1997.

Fig. 1shows a plan view of the physical config-

uration of the four detectors in 1997.

The pointing and angular resolution of SPASE-

1 were measured with a pair of small atmospheric

Cherenkov telescopes[8]. Each telescope consisted

of a Fresnel lens with an aperture stop and a

photomultiplier. The zenith and azimuth of the

telescopes were measured with a lunar transit,

using a flat mirror to reflect the image of the moon

into the telescope aperture. Then cosmic-ray

showers detected by both SPASE-1 and the

Cherenkov telescopes were used to determine the

absolute pointing of the air shower array to

in zenith and

in azimuth. In addition, the

coincident events were used to make a direct

determination of the angular resolution of the air

shower array as a function of shower size. This

ARTICLE IN PRESS

−

600

−

500

−

400

−

300

−

200

−

100

200

−

400

−

200

400

600

800

Y (m)

X (m)

MAP of AMANDAB10, SPASE1, SPASE2

SPASE1

AMANDAB10

GASP

SPASE2

VULCAN

Fig. 1. Map showing locations of SPASE-1 and SPASE-2 relative to locations of AMANDA-B10 strings at the surface. The origin of

the local coordinate system for each SPASE array is marked with a red cross. The origin of the AMANDA coordinate system coincides

with string 4, and the positive

-axis is grid north. Azimuth is measured counter-clockwise from grid east. Thus the center of SPASE-2

is at 247

and the center of SPASE-1 at 327

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

349

confirmed indirect determinations of angular

resolution made by Monte Carlo simulations and

by the sub-array method

[2,5]. Absolute orienta-

tion of SPASE-2 was determined by conventional

surveying techniques and its angular resolution by

use of the indirect methods proven by SPASE-1.

The accuracy with which the surface arrays

determine the directions of air showers increases

from 3

at threshold to 1

for the larger showers

used here to study angular resolution of AMAN-

DA. The angular resolution as a function of

shower size is shown explicitly in Fig. 7 of Ref. [5]

as the half-angle of a cone that contains 63% of

the events. This definition is appropriate for a two-

dimensional Gaussian distribution. The rms error

in location of shower cores decreases from 8 m at

threshold to

5 m for the higher energy showers

(Fig. 6 of Ref. [5]).

The GASP telescope [7] consisted of 10 mirrors,

each viewed by 2 photomultiplier tubes, one

pointing on-source and the other pointing 2

off-source. In the 1997 run

[9]

the ‘‘source’’ was

opposite the direction to the center of the

instrumented portion of AMANDA-B10. The

off-source direction was chosen to select events

pointed toward the top of the instrumented

volume. The GASP instrument had an optical

angular acceptance of 0

;

an angular resolution

of about one degree for cosmic-ray showers, with

an energy threshold of approximately 1–2 TeV

1.2. Description of AMANDA

The evolution and operation of the AMANDA

detector are described in Ref. [6]. In this paper we

concentrate on data obtained with AMANDA-

B10, which consists of 10 vertical strings of

detectors located as shown in the plan view of

Fig. 1. Each string is instrumented with OMs at

assigned depths between 1.5 and 2 km in clear

Antarctic ice.

Altogether there are 302 optical sensors in

AMANDA-B10, forming an instrumented cylin-

der of ice approximately 500 m high and 120 m in

diameter. A line from the center of AMANDA-

B10 to the center of SPASE-2 has a zenith angle of

The corresponding angle to SPASE-1 is 27

The combination of a surface array of area

with

the array deep in the ice constitutes a three-

dimensional cosmic-ray detector with an accep-

tance of

cos

where

is the projected area of AMANDA-

B10 viewed at a zenith angle

from the surface

array and

is the distance between the centers of

the two detectors. The solid angles of the

acceptance cones are small,

0015 sr and

005 sr for SPASE-1/AMANDA-B10 and

SPASE-2/AMANDA-B10, respectively. Given the

dimensions listed above,

50 m

sr and

100 m

Coincidence rates can be esti-

mated by multiplying the acceptance with the flux

of cosmic-rays with energy above the threshold of

each array. With thresholds for full efficiency of

approximately 200 TeV

;

the coincidence rate is

around 10

Hz for SPASE-2-AMANDA-B10.

1.3. Shower phenomenology in SPASE and

AMANDA

A shower initiated by a high-energy primary

cosmic-ray nucleus consists of a disk of relativistic

secondary particles (mostly electrons and posi-

trons with

100 MeV) propagating through the

atmosphere at nearly the speed of light. The

shower direction is reconstructed from the arrival

times of the shower front at the detectors. A

measure of the primary energy is given by the

density of charged particles measured at a nominal

perpendicular distance from the shower core. The

nominal core distance used for the SPASE arrays

is 30 m

;

and the particle density in units of vertical

equivalent muons per m

at 30 m is denoted

It is also possible to use assumed or measured

lateral distributions to obtain a fitted shower size.

The relation between

and primary energy for

simulated protons and iron primaries with

100 TeV and

is shown in Fig. 2. Note that,

as a consequence of fluctuations on a steep

spectrum, average energy as a function of

is not the inverse of average

as a function of

energy. Fluctuations are especially important near

threshold. The upper panels of the figure illustrate

ARTICLE IN PRESS

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

350

how the reconstruction efficiency falls off in the

threshold region.

To relate measured quantities to physical

properties of the showers as in

Fig. 2, we use a

Monte Carlo simulation. Showers are generated

with energies from 100 TeV to 100 PeV using a

modified version of MOCCA

[10]

calling the

QGSJET98

[11]

hadronic interaction model. We

use MOCCA for consistency with previous analy-

sis of the SPASE/VULCAN data [12]. It has been

updated to include separate treatment of kaons

and consistent treatment of interactions of pri-

mary nuclei. The hadronic event generator

QGSJET98 is generally considered to give the best

representation of hadronic interactions in this

energy region [13]. High-energy muons are propa-

gated through the ice to the depth of AMANDA-

B10 using MUDEDX

[14]

to make a stochastic

calculation of muon energy losses. The response of

AMANDA to light radiated by the muons is

evaluated by the program AMASIM

[15]. This

program uses pre-calculated tables to simulate the

arrival times and amplitudes of photo-electrons at

the anodes of the photomultipliers. AMASIM

then uses parameters of the hardware to generate a

realistic response of the detector to the muons.

For an array of 0

detectors on a 30 m

triangular grid, the threshold corresponds to

showers with a density

For cosmic-ray

protons this corresponds to a primary energy of

50 TeV

;

but showers in the threshold range are

poorly reconstructed, having an uncertainty in

direction of

to 4

[5]. The accuracy improves

for

150 TeV for protons

ARTICLE IN PRESS

Number of showers

log

(E(GeV))

log

(S30)

log

(S30)

proton

iron

Number of showers

log

(S30)

log

(E(GeV))

log

(E(GeV))

proton

iron

Fig. 2. Distributions of primary energy and

(upper panels), and relationships between them (lower panels), for protons (solid,

open circles) and iron (dashed, stars) simulation. The lower panels show

log

ÞÞ

vs. logarithm of energy (left) and

log

vs. logarithm of

(right).

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

351

and

300 TeV for Fe) and to

for showers

with energy above 1 PeV

Since many properties of

cosmic-ray showers are energy-dependent (as well

as the detector response of both SPASE and

AMANDA), in what follows we divide the

complete set of data and Monte Carlo into four

large bins of

;

and

The lowest-energy

bin includes events with energies up to

300 TeV

(depending on mass of the primary nucleus), while

the highest-energy bin is roughly the region of the

knee (1–10 PeV).

High energy muons in the shower core with

sufficient energy at production propagate down

through the ice and are visible in AMANDA for

showers with trajectories within the acceptance

cone. The minimum energy of a muon required to

reach the top of AMANDA-B10 from SPASE-2 is

about 370 GeV

;

and muons with

540 GeV at

production can penetrate through it. Since the

lateral distribution of the muon bundles is

determined primarily from the transverse momen-

tum of the pions at production 10–20 km above

the ground, the muon bundles are characterized by

a typical radius of

20 m at the top of AMAN-

DA-B10 and

10 m at the bottom. About half the

muons that reach the top of AMANDA-B10 range

out inside it. In Fig. 3 we show simulated lateral

distributions of muons for proton and iron

showers at 1730 m depth for the standard four

bins of

The intercept gives the average

muon multiplicity for each class of events. For a

given

showers generated by heavy primaries

give more muons than showers generated by

protons. There are two reasons for this. First, for

the same primary energy, heavy primary nuclei

produce more muons because shower pions are

more likely to decay than interact (assuming the

ARTICLE IN PRESS

0 255075

0 255075 100

0 255075

distance to primary track (m)

muons/event outside R

distance to primary track (m)

muons/event outside R

distance to primary track (m)

muons/event outside R

distance to primary track (m)

muons/event outside R

0 255075

S(30) = 25

−

= 0.6

−

1.4 PeV

= 1.0

−

2.0 PeV

S(30) > 50

> 1.4 PeV

> 2.0 PeV

S(30) = 10

−

= 250

−

600 TeV

= 600

−

1000 TeV

S(30) < 10

< 250 TeV

< 600 TeV

100

Fig. 3. Integral lateral distribution of muons at the depth of AMANDA for simulated proton (dashed) and iron (dotted) showers. The

plot shows the average number of muons at distances larger than a given radius for the four

intervals described in the text. The

intercept at zero radius is the average muon multiplicity for the each class of events. Where the histograms meet the horizontal line

marks the distance beyond which there is on average less than one muon.

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

352

energy per nucleon is high enough to be outside

the threshold region)

[16]. Second, for a given

the energy is higher for a heavy nucleus than

for protons, as shown in Fig. 2 and by the energy

ranges listed on the plots in 3.

Whenever an air shower triggers one of the

surface arrays, a trigger window is opened to read

out AMANDA. The window is 32

s in length,

and its delay is adjusted to account for the

propagation time of the muons in the air shower

core to reach AMANDA and for the signals to

propagate back up the AMANDA cables. The

total acceptance of SPASE-2–AMANDA-B10 is

small. As a consequence, most showers recon-

structed by SPASE do not trigger AMANDA.

Coincident events occur only when the direction of

the air shower at the surface defines a trajectory

that extends through or near AMANDA. Coin-

cidences are identified offline by making use of the

GPS time tags of the surface and AMANDA

events.

2. Angular resolution and pointing of

AMANDA-B10

Most, but not all, AMANDA modules face

downward, in keeping with its primary function as

a neutrino telescope. The detector nevertheless has

good sensitivity to downgoing muons, as illu-

strated by the fact that hit probability for upward

and downward facing OMs is similar in air

showers observed in coincidence by SPASE and

AMANDA. Thus downgoing events can be used

to calibrate the response of AMANDA to both

downward and upward events. Because air

showers that trigger SPASE typically contain

several muons with sufficient energy to reach the

depth of AMANDA, however, the downgoing

coincident events are in a different class from both

single downgoing atmospheric muons and neutri-

no-induced upgoing muons.

A straightforward measure of the angular

resolution and pointing accuracy of AMANDA

is obtained by comparing the directions assigned

by the AMANDA reconstruction algorithm for

coincident events with the directions assigned

independently to the same events by SPASE. For

this analysis we selected a sample of events well-

reconstructed in both SPASE and AMANDA.

The cuts on the surface parameters are:

;

shower core within the perimeter of the array, and

projected shower core passing inside the AMAN-

DA-B10 cylinder. In AMANDA various quality

cuts are used for analysis of neutrino-induced

upward muons. An inverted version of these

quality cuts was used here for downgoing events.

Specifically, we require a sufficiently downgoing

fitted zenith angle, a large number of ‘‘direct’’ hits

(meaning hits with an arrival time close to the

expected arrival time of the Cherenkov cone), a

long length of the projection of these direct hits

onto the track, a small difference between zenith

angles of tracks reconstructed in two different

ways, and a sufficiently large velocity of the linefit.

Fig. 4

shows the distributions of the angle in

space between the direction assigned by the surface

air shower arrays and the direction assigned by

AMANDA-B10 for coincidences with SPASE-1

and with SPASE-2. As a measure of the width of

the distribution of space-angle difference, we use

the half-angle of the cone that contains 63% of the

events,

The values are 4

and 5

;

respec-

tively for SPASE-1 and SPASE-2 coincidences.

Given the estimate of

for SPASE, we can

estimate the accuracy of AMANDA-B10 for

reconstructing direction air shower cores that

trigger SPASE and AMANDA as

;

where

is obtained from the distributions

shown in

Fig. 4. This gives

B10

for

events from the direction of SPASE-1 and

from the direction of SPASE-2.

As in

Refs. [17,18], we find, however, that the

space-angle distribution is not fit well by a single

two-dimensional Gaussian, but requires two com-

ponents with comparable weights. Such two-

component fits are shown here by the curves in

Fig. 4.InRef. [17]the need for two components

was traced to a degradation of the angular

resolution for high-energy muons based on simu-

lations of neutrino-induced muons. The situation

here is further complicated by the possibility of

multiple muons. The medians of the distributions

in Fig. 4 are 3

and 3

for SPASE-1 and

SPASE-2, respectively. These values characterize

the distributions of differences in direction

ARTICLE IN PRESS

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

353

between two independent experimental measure-

ments of the same events, one with a surface array,

the other with AMANDA-B10. The correspond-

ing median of the difference between true direction

and reconstructed direction found in the simula-

tion of Refs. [17,18] is 3

Thus, we confirm by an

independent analysis the results for resolution used

in the AMANDA point source search [18].

We have also compared the absolute directions

assigned by SPASE with those assigned by

AMANDA-B10 to see if there is a systematic

offset in the absolute pointing. Although there is

no significant offset in azimuth, the zenith angle

distribution shows a systematic average offset of

;

as shown in Fig. 5. To investigate whether

this offset may be in part due to the lateral extent

of the muon bundles, we can also compare with a

sample of smaller showers which generally give

single muons at AMANDA. This is possible

because the GASP atmospheric Cherenkov tele-

scope

[7]

was also running during 1997. Because

the threshold of GASP for cosmic-ray showers is

significantly lower than for the air shower detec-

tors, GASP coincidences consist mostly of single

muons at AMANDA. These events therefore have

different systematics from SPASE events.

Fig. 5

shows the measurements of absolute

pointing relative to the three surface detectors. The

two GASP cameras give different offsets. This is

not understood, but we note that the two cameras

point at different portions of AMANDA

[9].In

particular, the camera focused on events pointed

near the top of the instrumented volume of

AMANDA-B10 shows the larger offset. The

SPASE-1 and SPASE-2 offsets can vary anywhere

between 0

and 2

depending on the cut values

required in the AMANDA quality parameters

ARTICLE IN PRESS

Azimuth Error (degrees)

Zenith Error (degrees)

GASP

SPASE1

SPASE2

5 4 3 2 1 0 1 2 3 4

Fig. 5. Three independent measurements of absolute pointing

accuracy (origin

perfect pointing). Gasp results from

Ref. [7]

shown separately for two Gasp cameras.

100

010 20 30

SPASE1

number of events

SPASE2

Space angle error (degrees)

010 20

Fig. 4. Distribution of difference between direction assigned by SPASE and that assigned by AMANDA-B10 for a sample of

coincident events, fit by a double-Gaussian.

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

354

described earlier. GASP, SPASE-1 and SPASE-2

all agree, however, in showing a small systematic

offset in zenith of about 1

relative to AMAN-

DA. Since GASP shows a similar offset to SPASE,

we conclude that the offset is not a consequence of

the spread of the muon bundles. Given the fixed

locations of the surface detectors, this experimen-

tal check of pointing is only possible for fixed

zenith angles.

Refs. [17,18]

include Monte Carlo

studies of the offset that independently confirm the

offset obtained from SPASE data and which

extend the analysis to all directions for single

muons.

The direction of the systematic offset shows that

AMANDA tends to assign a smaller zenith angle

than the surface detectors. A possible source of

this systematic effect is the long, narrow shape of

AMANDA-B10 coupled with the errors in the

direction as determined by SPASE. Since a thin

vertical detector reconstructs vertical events with

higher efficiency than oblique ones, the coinci-

dence sample is biased in favor of events in which

the true zenith angle is smaller than that assigned

by SPASE. The offset is substantially smaller than

the angular resolution of AMANDA-B10 and

small compared to the size of the point source

search bin, which has a half angle

[17,18].

3. Muon tomography

The response of the AMANDA optical modules

to muons in cores of air showers can be used to

map the deep array and study properties of the ice

in which they are embedded.

3.1. Muon survey of AMANDAB10

Two methods have been used to obtain a muon

survey of AMANDA OM locations. Both start

from the zenith and azimuth of showers as

determined by SPASE for events in which a parti-

cular OM in AMANDA-B10 registers a signal. In

the first method, we plot the distributions of zenith

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azimuth(¼)

AMANDA B10 optical module number

100

150 200 250 300

050

100

150 200 250 300

zenith(¼)

AMANDA B10 optical module number

fitted azimuth

expected azimuth

fitted zenith

expected zenith

340

335

330

325

320

315

310

Fig. 6. Muon survey of AMANDA B10 (view from SPASE-1).

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

355

and of azimuth of all coincident events in which a

particular AMANDA OM was hit. This is

repeated for each OM. For zenith angle, the

distributions obtained in this way are divided by

the zenith angle distribution for all SPASE triggers

in order to remove the bias associated with the

steep zenith-angle distribution convolved with the

resolution of SPASE. The fitted mean directions

(zenith and azimuth) are determined in this way

for each OM. Fig. 6 shows the result for the survey

of AMANDA-B10 from SPASE-1 using this

method. The fitted directions for each OM are

compared to the directions from the center of

SPASE-1 as determined from the AMANDA

survey.

SPASE-2 is larger and closer to AMANDA

than SPASE-1. Thus the approximation under-

lying the first method (that every trajectory passes

through the center of the surface array) introduces

relatively larger errors. We therefore adopted a

second survey method in which the expected

direction for each event was taken as the direction

from the shower core at the surface (as determined

by SPASE for the event) to the OM position as

determined from the AMANDA survey, which

consists of station surveys, drill log data and

internal laser calibrations [6]. The apparent direc-

tion for a particular event is then the measured

direction of the event as determined by SPASE.

For each OM the distributions of apparent minus

expected angle were fitted for zenith and azimuth

separately. For SPASE-1 the results are indistin-

guishable from

Fig. 6. The muon survey of

SPASE-2 using this event-by-event method is

shown in Fig. 7. The agreement with the nominal

OM locations is within

in azimuth (

laterally), and there is a 0

systematic offset in

zenith (bottom panel).

While the event-by-event method is geometri-

cally more accurate, the trigger biases due to the

steep zenith angle distribution have not been

explicitly removed (though the apparent-minus-

expected distributions for each OM are fitted to a

Gaussian plus a background which is allowed to

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azimuth(

)

AMANDA B10 optical module number

fitted azimuth

expected azimuth

265

260

255

245

240

235

050

100

150 200 250 300

fitted zenith

expected zenith

050

100

150 200 250 300

zenith(

)

AMANDA B10 optical module number

250

Fig. 7. Muon survey of AMANDA B10 (view from SPASE-2).

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

356

have a linear dependence on angle). To study these

systematic effects, we performed the same survey

with simulated data. The simulations show essen-

tially no offset in azimuth, as expected, while the

average 0

offset in zenith seen in the data is

reproduced. This gives confidence in the absolute

positions of both detector components.

3.2. Ice properties

The same data used for the survey of OMs can

be used to obtain a relative measure of attenuation

of light in the ice. This is done by comparing the

response of OMs at different depths to showers as

a function of impact parameter. Absorption of

light in the ice is dominated by dust, and modules

embedded in layers with more dust cannot see

events from as far away as those in clearer layers.

Since the impact parameter for each event is

determined by projecting the trajectory determined

by SPASE, the impact parameter distribution is

spread significantly compared to the true distribu-

tion. Rather than deconvolving the angular

resolution effect here, we simply show that the

ice properties revealed by the muons are qualita-

tively similar to those from laser studies [19].

To do this, we define a parameter

which is

determined by fitting the distribution of hit

probabilities for each OM to an exponential

distribution as a function of apparent impact

parameter. In this way, a value of

is determined

for each OM.

Fig. 8

shows

as a function of

depth. The prominent features of this plot match

up well in depth with variations in the optical

properties of south pole ice as determined from

completely independent methods. In Ref. [19], the

scattering coefficient of ice as a function of depth

was obtained by fitting arrival time distributions of

pulsed light sources sent and received between

AMANDA OMs at various separations but

similar depths. Depths of minimum and maximum

scattering found in that analysis correspond

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depth (m)

Fig. 8. A simple exponential fit to hit probability as a function of apparent impact parameter reflects the varying ice clarity as a

function of depth. See text for a definition of

The points A, B and Cindicate locations of dust layers described in

Ref. [19].

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

357

closely to maxima and minima, respectively, in

Fig. 8, as expected since scattering is proportional

to 1

4. Muon bundles in AMANDA

Ref. [1]

we use the muon bundles seen by

AMANDA in coincidence with air showers

measured by SPASE for a study of primary

cosmic-ray composition. To do this we need to

measure the lateral distribution of the light

generated by the muons in AMANDA, which

requires knowing the trajectory of each coincident

event as accurately as possible. Rather than using

the trajectory determined by SPASE alone or by

AMANDA alone, we fix the location of the

trajectory to coincide with the core location at

the surface as measured by SPASE. Then the

direction is determined with the AMANDA

reconstruction program subject to this constraint.

Fig. 9

shows examples of the measured lateral

distributions of pulse heights from light generated

by six large muon bundles in AMANDA for which

the trajectories were determined in this way. The

well-determined lateral distribution of the muon

light pool measured by AMANDA demonstrates

that the combined track fit works and that the

light pool produced by a muon bundle in

AMANDA can be measured well. Such measure-

ments form the basis of the composition analysis

in Ref. [1].

References

[1] K. Rawlins for the SPASE and AMANDA Collabora-

tions, in: T. Kajita, et al. (Eds.), Proceedings of the 28th

International Cosmic Ray Conference, Tsukuba, Japan,

Vol. 1, Universal Academy Press, Tokyo, 2003, p. 173

(Expanded version to be submitted for publication.).

[2] N.J.T. Smith, et al., Nucl. Instr. and Meth. A 276 (1989)

622.

[3] J. Beaman, et al., Phys. Rev. D 48 (1993) 4495.

[4] J. van Stekelenborg, et al., Phys. Rev. D 48 (1993) 4504.

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020 40 60 80

020 40 60 80 100

020 40

020 40 60 80

core distance (m)

OM amplitude

core distance (m)

OM amplitude

core distance (m)

OM amplitude

core distance (m)

OM amplitude

core distance (m)

OM amplitude

core distance (m)

OM amplitude

020 40 60 80

100

100 100

Fig. 9. Lateral distribution of the Cherenkov light signal generated by six muon bundles at AMANDA. Core distance is the

perpendicular distance of each OM from the trajectory of the shower core. From the plot of

vs.

inFig. 2, the corresponding

estimates of primary energy for these events are in the range 1–10 PeV

J. Ahrens et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 347–359

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R. Kopp, W. Lohmann, R. Voss, MUDEDX: parame-

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[15] S. Hundertmark, Ph.D. Thesis, Humboldt-Universit

at,

Berlin, 1999, available at

http://amanda.berkeley.edu/

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