Measurement of South Pole ice transparency with the IceCube LED calibration system

1.2 MB·English

by  IceCube Collaboration

Measurement of South Pole ice transparency with the IceCube
LED calibration system
M.G.Aartsenb,R.Abbasiaa,Y.Abdouv,M.Ackermannao,J.Adamso,J.A.Aguilaru,
M.Ahlersaa,D.Altmanni,J.Auffenbergaa,X.Baiae,1,M.Bakeraa,S.W.Barwickw,V.Baumab,
R.Bayg,J.J.Beattyq,r,S.Bechetl,J.BeckerTjusj,K.-H.Beckeran,M.Bellal,
M.L.Benabderrahmaneao,S.BenZviaa,J.Berdermannao,P.Berghausao,D.Berleyp,
3
E.Bernardiniao,A.Bernhardad,D.Bertrandl,D.Z.Bessony,G.Binderh,g,D.Bindigan,
1
0 M.Bissoka,E.Blaufussp,J.Blumenthala,D.J.Boersmaam,S.Bohaichukt,C.Bohmah,
2 D.Bosem,S.Bo¨serk,O.Botneram,L.Brayeurm,A.M.Browno,R.Bruijnx,J.Brunnerao,
n S.Buitinkm,M.Carsonv,J.Caseye,M.Casierm,D.Chirkinaa,5,∗,B.Christyp,K.Clarkal,
a F.Clevermanns,S.Cohenx,D.F.Cowenal,ak,A.H.CruzSilvaao,M.Danningerah,
J J.Daughheteee,J.C.Davisq,C.DeClercqm,S.DeRidderv,P.Desiatiaa,M.deWithi,

2 T.DeYoungal,J.C.D´ıaz-Ve´lezaa,M.Dunkmanal,R.Eaganal,B.Eberhardtab,J.Eischaa,
2 R.W.Ellsworthp,S.Eulera,P.A.Evensonae,O.Fadiranaa,A.R.Fazelyf,A.Fedynitchj,

J.Feintzeigaa,T.Feuselsv,K.Filimonovg,C.Finleyah,T.Fischer-Waselsan,S.Flisah,
]
M A.Franckowiakk,R.Frankeao,K.Frantzens,T.Fuchss,T.K.Gaisserae,J.Gallagherz,
L.Gerhardth,g,L.Gladstoneaa,T.Glu¨senkampao,A.Goldschmidth,G.Golupm,
I
. J.A.Goodmanp,D.Go´raao,D.Grantt,A.Großad,M.Gurtneran,C.Hah,g,A.HajIsmailv,
h
p A.Hallgrenam,F.Halzenaa,K.Hansonl,D.Heeremanl,P.Heimanna,D.Heinena,K.Helbingan,
- R.Hellauerp,S.Hickfordo,G.C.Hillb,K.D.Hoffmanp,R.Hoffmannan,A.Homeierk,
o
K.Hoshinaaa,W.Huelsnitzp,2,P.O.Hulthah,K.Hultqvistah,S.Hussainae,A.Ishiharan,
r
t E.Jacobiao,J.Jacobsenaa,G.S.Japaridzed,K.Jeroaa,O.Jlelativ,B.Kaminskyao,A.Kappesi,
s
a T.Kargao,A.Karleaa,J.L.Kelleyaa,J.Kirylukai,F.Kislatao,J.Kla¨san,S.R.Kleinh,g,
[ J.-H.Ko¨hnes,G.Kohnenac,H.Kolanoskii,L.Ko¨pkeab,C.Kopperaa,S.Kopperan,

1 D.J.Koskinenal,M.Kowalskik,M.Krasbergaa,G.Krollab,J.Kunnenm,N.Kurahashiaa,
v T.Kuwabaraae,M.Labarem,H.Landsmanaa,M.J.Larsonaj,M.Lesiak-Bzdakai,J.Leutead,
1 J.Lu¨nemannab,J.Madsenag,R.Maruyamaaa,K.Masen,H.S.Matish,F.McNallyaa,
6 K.Meagherp,M.Merckaa,P.Me´sza´rosak,al,T.Meuresl,S.Miareckih,g,E.Middellao,N.Milkes,
3
J.Millerm,L.Mohrmannao,T.Montaruliu,3,R.Morseaa,R.Nahnhauerao,U.Naumannan,
5
H.Niederhausenai,S.C.Nowickit,D.R.Nygrenh,A.Obertackean,S.Odrowskiad,A.Olivasp,
.
1 M.Olivoj,A.O’Murchadhal,L.Paula,J.A.Pepperaj,C.Pe´rezdelosHerosam,C.Pfendnerq,
0
D.Pieloths,N.Pirkao,J.Posseltan,P.B.Priceg,G.T.Przybylskih,L.Ra¨dela,K.Rawlinsc,
3
1 P.Redlp,E.Resconiad,W.Rhodes,M.Ribordyx,M.Richmanp,B.Riedelaa,J.P.Rodriguesaa,
: C.Rottq,T.Ruhes,B.Ruzybayevae,D.Ryckboschv,S.M.Sabaj,T.Salamehal,H.-G.Sanderab,
v
M.Santanderaa,S.Sarkaraf,K.Schattoab,M.Scheela,F.Scheriaus,T.Schmidtp,M.Schmitzs,
i
X S.Schoenena,S.Scho¨nebergj,L.Scho¨nherra,A.Scho¨nwaldao,A.Schukrafta,L.Schultek,
r O.Schulzad,D.Seckelae,S.H.Seoah,Y.Sestayoad,S.Seunarineag,C.Sherematat,
a
M.W.E.Smithal,M.Soirona,D.Soldinan,G.M.Spiczakag,C.Spieringao,M.Stamatikosq,4,
T.Stanevae,A.Stasikk,T.Stezelbergerh,R.G.Stokstadh,A.Sto¨ßlao,E.A.Strahlerm,
R.Stro¨mam,G.W.Sullivanp,H.Taavolaam,I.Taboadae,A.Tamburroae,S.Ter-Antonyanf,
S.Tilavae,P.A.Toaleaj,S.Toscanoaa,M.Usnerk,D.vanderDrifth,g,N.vanEijndhovenm,
A.VanOverloopv,J.vanSantenaa,M.Vehringa,M.Vogek,M.Vraeghev,C.Walckah,
T.Waldenmaieri,M.Wallraffa,R.Wassermanal,Ch.Weaveraa,M.Wellonsaa,C.Wendtaa,
S.Westerhoffaa,N.Whitehornaa,K.Wiebeab,C.H.Wiebuscha,D.R.Williamsaj,H.Wissingp,
M.Wolfah,T.R.Woodt,C.Xuae,D.L.Xuaj,X.W.Xuf,J.P.Yanezao,G.Yodhw,S.Yoshidan,
1
P.Zarzhitskyaj,J.Ziemanns,S.Zierkea,A.Zillesa,M.Zollah
aIII.PhysikalischesInstitut,RWTHAachenUniversity,D-52056Aachen,Germany
bSchoolofChemistry&Physics,UniversityofAdelaide,AdelaideSA,5005Australia
cDept.ofPhysicsandAstronomy,UniversityofAlaskaAnchorage,3211ProvidenceDr.,Anchorage,AK99508,USA
dCTSPS,Clark-AtlantaUniversity,Atlanta,GA30314,USA
eSchoolofPhysicsandCenterforRelativisticAstrophysics,GeorgiaInstituteofTechnology,Atlanta,GA30332,USA
fDept.ofPhysics,SouthernUniversity,BatonRouge,LA70813,USA
gDept.ofPhysics,UniversityofCalifornia,Berkeley,CA94720,USA
hLawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA
iInstitutfu¨rPhysik,Humboldt-Universita¨tzuBerlin,D-12489Berlin,Germany
jFakulta¨tfu¨rPhysik&Astronomie,Ruhr-Universita¨tBochum,D-44780Bochum,Germany
kPhysikalischesInstitut,Universita¨tBonn,Nussallee12,D-53115Bonn,Germany
lUniversite´LibredeBruxelles,ScienceFacultyCP230,B-1050Brussels,Belgium
mVrijeUniversiteitBrussel,DienstELEM,B-1050Brussels,Belgium
nDept.ofPhysics,ChibaUniversity,Chiba263-8522,Japan
oDept.ofPhysicsandAstronomy,UniversityofCanterbury,PrivateBag4800,Christchurch,NewZealand
pDept.ofPhysics,UniversityofMaryland,CollegePark,MD20742,USA
qDept.ofPhysicsandCenterforCosmologyandAstro-ParticlePhysics,OhioStateUniversity,Columbus,OH43210,
USA
rDept.ofAstronomy,OhioStateUniversity,Columbus,OH43210,USA
sDept.ofPhysics,TUDortmundUniversity,D-44221Dortmund,Germany
tDept.ofPhysics,UniversityofAlberta,Edmonton,Alberta,CanadaT6G2G7
uDe´partementdephysiquenucle´aireetcorpusculaire,Universite´deGene`ve,CH-1211Gene`ve,Switzerland
vDept.ofPhysicsandAstronomy,UniversityofGent,B-9000Gent,Belgium
wDept.ofPhysicsandAstronomy,UniversityofCalifornia,Irvine,CA92697,USA
xLaboratoryforHighEnergyPhysics,E´colePolytechniqueFe´de´rale,CH-1015Lausanne,Switzerland
yDept.ofPhysicsandAstronomy,UniversityofKansas,Lawrence,KS66045,USA
zDept.ofAstronomy,UniversityofWisconsin,Madison,WI53706,USA
aaDept.ofPhysicsandWisconsinIceCubeParticleAstrophysicsCenter,UniversityofWisconsin,Madison,WI53706,
USA
abInstituteofPhysics,UniversityofMainz,StaudingerWeg7,D-55099Mainz,Germany
acUniversite´deMons,7000Mons,Belgium
adT.U.Munich,D-85748Garching,Germany
aeBartolResearchInstituteandDepartmentofPhysicsandAstronomy,UniversityofDelaware,Newark,DE19716,
USA
afDept.ofPhysics,UniversityofOxford,1KebleRoad,OxfordOX13NP,UK
agDept.ofPhysics,UniversityofWisconsin,RiverFalls,WI54022,USA
ahOskarKleinCentreandDept.ofPhysics,StockholmUniversity,SE-10691Stockholm,Sweden
aiDepartmentofPhysicsandAstronomy,StonyBrookUniversity,StonyBrook,NY11794-3800,USA
ajDept.ofPhysicsandAstronomy,UniversityofAlabama,Tuscaloosa,AL35487,USA
akDept.ofAstronomyandAstrophysics,PennsylvaniaStateUniversity,UniversityPark,PA16802,USA
alDept.ofPhysics,PennsylvaniaStateUniversity,UniversityPark,PA16802,USA
amDept.ofPhysicsandAstronomy,UppsalaUniversity,Box516,S-75120Uppsala,Sweden
anDept.ofPhysics,UniversityofWuppertal,D-42119Wuppertal,Germany
aoDESY,D-15735Zeuthen,Germany
Abstract
The IceCube Neutrino Observatory, approximately 1 km3 in size, is now complete with 86
strings deployed in the Antarctic ice. IceCube detects the Cherenkov radiation emitted by
charged particles passing throughor created in the ice. To realize the full potential of the de-
tector, the properties of light propagation in the ice in and around the detector must be well
understood. Thisreportpresentsa new methodoffitting the modelof lightpropagationin the
2
icetoadatasetofin-situlightsourceeventscollectedwithIceCube.Theresultingsetofderived
parameters, namely the measured values of scattering and absorption coefficients vs. depth, is
presentedandacomparisonofIceCubedatawithsimulationsbasedonthenewmodelisshown.
1. Introduction
IceCubeisacubic-kilometer-scalehigh-energyneutrinoobservatorybuiltatthegeographic
SouthPole[1](seeFig.1).AprimarygoalofIceCubeistoelucidatethemechanismsforproduc-
tionofhigh-energycosmicraysbydetectinghigh-energyneutrinosfromastrophysicalsources.
IceCube uses the 2.8 km thick glacial ice sheet as a medium for producing Cherenkov light
emittedbychargedparticlescreatedwhenneutrinosinteractintheiceornearbyrock. Neutrino
interactionscancreatehigh-energymuons,electronsortauleptons,whichmustbedistinguished
fromabackgroundofdowngoingatmosphericmuonsbasedonthepatternofemittedCherenkov
light. Thislightisdetectedbyanembeddedarrayof5160opticalsensors(digitalopticalmod-
ules, orDOMs forshort), 4680of which are deployedat depths of 1450- 2450m andspaced
17mapartalong78verticalcables(strings).Thestringsarearrangedinatriangularlatticewith
ahorizontalspacingofapproximately125m.Theremaining480sensorsaredeployedinamore
compactgeometryformingthe centerof the DeepCorearray [2]. The IceCubeopticalsensors
areremotely-controlledautonomousdetectionunitswhichdigitizethedata. Theyincludelight-
emittingdiodes(LEDs)whichmaybeusedasartificialin-situlightsources. AlsoshowninFig.
1 is the location of the AMANDA-II neutrino telescope. AMANDA-II was the precursor for
IceCubeandwascomposedof677opticalsensorsorganizedalong19strings,withmostofthe
sensors located at depthsof 1500to 2000m. It operatedas a part of the IceCube observatory
untilitwasdecommissionedinMay2009.
Cherenkovphotonsareemittedwith a characteristicwavelengthdependenceof1/λ2 in the
wavelength range of 300-600 nm, which includes the relevant sensitivity region of the photo-
sensors. Photonsareemittedinaconearoundthedirectionofparticlemotionwithanopening
angle,determinedbythespeedoftheparticleandrefractiveindexoftheice[3],ofabout41 for
◦
relativisticparticles. Asthephotonspropagatefromthepointofemissiontothereceivingsen-
sor,theyareaffectedbyabsorptionandscatteringintheice. Thesepropagationeffectsmustbe
consideredforbothsimulationandreconstructionofIceCubedataandthusneedtobecarefully
modeled.Theimportantparameterstodescribephotonpropagationinatransparentmediumare:
theaveragedistancetoabsorption,theaveragedistancebetweensuccessivescattersofphotons,
andtheangulardistributionofthenewdirectionofaphotonateachgivenscatteringpoint. This
workpresentsanew,global-fitapproachwhichachievesanimproveddescriptionofexperimental
data.
To determine the ice parameters, dedicated measurementsare performedwith the IceCube
detector. PhotonsareemittedbytheLEDsinDOMsandrecordedbyotherDOMs,assketched
Correspondingauthor
∗
1PhysicsDepartment,SouthDakotaSchoolofMinesandTechnology,RapidCity,SD57701,USA
2LosAlamosNationalLaboratory,LosAlamos,NM87545,USA
3alsoSezioneINFN,DipartimentodiFisica,I-70126,Bari,Italy
4NASAGoddardSpaceFlightCenter,Greenbelt,MD20771,USA
[email protected]
PreprinttobesubmittedtoNuclearInst.andMethodsinPhysicsResearch,A January24,2013
Figure1: TheIceCubeNeutrinoObservatory,finalconfiguration. AlsoshownistheAMANDAarray,pre-
cursortoIceCube,whichendedoperationin2009.
30
122 m
s
bin25
s
n
0 20
5
n
s i15
n 217 m (x10)
o
ectr10
el
o
hot 5
p
0 1000 2000 3000 4000 5000
time from the flasher event [ ns ]
Figure2: Left(a): simplifiedschematics oftheexperimental setup: theflashingsensorontheleftemits
photons,whichpropagatethroughiceandaredetectedbyareceivingsensorontheright.Right(b):example
photonarrivaltimedistributionsatasensorononeoftheneareststrings(122maway)andononeofthe
next-to-neareststrings(217maway;histogramvaluesaremultipliedbyafactorof10forclarity). Dashed
linesshowdataandsolidlinesshowsimulationbasedonthemodelofthiswork(withbestfitparameters).
Thegoalofthisworkistofindthebest-fiticeparametersthatdescribethesedistributionsasobservedindata
simultaneouslyforallpairsofemittersandreceivers.
inFig.2a. Therecordeddataincludethetotalcharge(correspondingtothenumberofarriving
photons)andphotonarrivaltimes, shownin Fig. 2b. A data set thatcoversall detectordepths
wasproduced. Aglobalfitofthesedatawasperformed,andtheresultisasetofscatteringand
absorptionparametersthat best describesthe fulldata set. The AMANDA Collaborationused
an analysis based on separate fits to data for individual pairs of emitters and receivers [4] to
4
measuretheopticalpropertiesoftheice. Thesefits useddatatakenatverylowlightlevels, to
avoidmulti-photonpileupdetectoreffects.
The relevantdetectorinstrumentationis describedin Section 2 of this paper. Section 3 in-
troduces the data set. The parameterization for modeling the ice surrounding the detector is
describedin Section4, while Section5 discussesthe simulation. Thelikelihoodfunctionused
tocomparedataandsimulationisdiscussedinSections6and7,andSection8explainshowthe
searchforthebestsolutionwasperformed. Section9comparestheresultwithanindependent
probeofthedustconcentrationinice[5]. Finally,Section 10discussestheuncertaintiesofthe
measurement,Section11presentsdata-simulationcomparisons,andSection12summarizesthe
result.
2. Instrumentation
Thedataforthisanalysiswereobtainedin2008whenIceCubeconsistedof40strings,each
with 60 DOMs, as shownin Fig. 3. Each of the DOMs consists of a 10” photomultipliertube
(PMT)[6]facingdownwardsandseveralelectronicsboardsenclosedinaglasspressuresphere
[1]. ThemainboardoftheelectronicsincludestwotypesofdigitizersforrecordingPMTwave-
formsaswellastimestamping,controlandcommunications[7]. Thefirst427nsofeachwave-
formisdigitizedat300megasamplespersecondbyfastATWDchips(analogtransientwaveform
digitizer,see[7]),andlongerdurationsignalsarerecordedat25megasamplespersecondbythe
fast ADC(fastanalog-to-digitalconverter,orfADCforshort)chips. Thesystem is capableof
resolvingchargeofupto300photoelectronsper25nswithprecisionlimitedonlybytheprop-
ertiesofthePMTs(i.e.,1photoelectronisresolvedwith 25%uncertaintyincharge).Boththe
∼
ATWDandfADCuse10bitsforamplitudedigitization.However,theATWDusesthreeparallel
channelswithdifferentgains(withafactorofabout8between)andhasa finertimeresolution
thanthefADC(roughly3.3vs.25nsbinwidth). ThemainboardcontainstwoATWDchipson
eachDOM,ensuringthatawaveformcanberecordedwithonechipwhiletheotheroneisread
out,thusreducingthesensordeadtime.
Each DOM includes12 LEDs on a “flasherboard”that producepulsed light detectableby
otherDOMslocatedupto 0.5kmaway. Theprimarypurposeofthemeasurementswith these
flashersiscalibrationofthedetector. Thesecalibrationstudiesincludedeterminingthedetector
geometry,verifyingthecalibrationoftimeoffsetsandthetimeresolution,verifyingthelinearity
of photonintensity measurement, and extracting the opticalpropertiesof the detectorice (this
paper).
Dependingon the intended application, flasher pulses can be programmedwith rates from
1.2Hzto610Hz,durationsofupto70ns,andLEDcurrentsupto240mA.Thecorresponding
total output from each LED ranges from below 106 to about 1010 photons. The programmed
current pulse is applied to each individualLED througha high-speed MOSFET (metal-oxide-
semiconductorfield-effecttransistor)driverwithaseriesresistor. Thevoltageacrosstheresistor
isrecordedbytheDOM’swaveformdigitizertopreciselydefinetheonsetofeachpulse.Figure4
showslaboratorymeasurementsoftheopticaloutputtime profilesfromshortandwidepulses.
Pulsesexhibitacharacteristicrise timeof3–4nsanda smallafterglow,decayingwith a 12ns
timeconstant. Thenarrowestpulsesachievablehaveafullwidthathalfmaximum(FWHM)of
6ns.
The wavelength spectrum has been measured for the LED light exiting the glass pressure
sphere and was found to be centered at 399 nm with a FWHM of 14 nm (see Fig. 5). This
wavelength was chosen to approximatethe typical wavelengthof detected Cherenkovphotons
5
600
N
[]y m 123450000000000 606857256169573662474057476347515758644765266457735764678458674W9594S050E z, m ---211086000000
0 38 39
-100 29 30 -2200
2010 2009
-200 21
-2400
-300
-400 -200 0 200 400 600 500 500
x [ m ] 250 0 0
run 111741 event 1407319
Figure3:Left:TopviewlayoutofIceCubeinthe40-stringconfigurationin2008. String63,forwhichthe
DOMsemittedflashinglightinthestudypresentedhere,isshowninblack.Thenearest6stringsareshown
inbrown. Thedashedlinesandnumbers2009and2010intheleftfigureindicatetheapproximatelocation
ofthedetectorpartsdeployedduringthoseyears.Right:atypicalDOMflasherevent,DOM46onstring63
flashing.ThelargercirclesrepresentDOMsthatrecordedlargernumbersofphotons.Thearrivaltimeofthe
earliestphotonineachDOMisindicatedwithcolor: earlytimesareshowninredwhilelatetimestrendto
blue.
Figure4: Flasherlight outputtimeprofileforpulses ofminimumandmaximumwidth. Therelative height ofthe
shortpulsehasbeenscaledsotheleadingedgesarecomparable. ThismeasurementwasperformedusingasmallPMT
(HamamatsuR1450)afteropticalattenuationofthepulsestofacilitatecountingofindividualphotons.
(as discussed and shown in Fig. 8 below). To supplement data from the standard flashers, 16
specialDOMswereconstructedanddeployedwithLEDsthatemitat340nm,370nm,450nm,
and500nm. Datafromthesespecialflasherswerenotusedintheanalysisofthispaperbutwill
beusedinfutureanalysesofwavelength-dependenteffects.
The12LEDsineachDOMareaimedinsixdifferentazimuthangles(with60 spacing)and
◦
alongtwodifferentzenithangles. Aftercorrectingforrefractionatinterfacesbetweenair,glass
and ice, the angular emission profiles peak along the horizontal direction for the 6 horizontal
LEDsand48 abovethehorizontalforthe6tiltedLEDs. Theangularspreadisreducedbythe
◦
refractionandismodeledusinga2-DGaussianprofilewithσ=10 aroundeachpeakdirection.
◦
DuringtheDOMdeploymentandfreeze-inwithintheglacialicesheet,theazimuthalorientations
6
LE(cid:6)(cid:7)(cid:8)t(cid:9)(cid:8)t(cid:10)(cid:9)(cid:0)(cid:11)t(cid:12)(cid:8)matM(cid:13)t(cid:0)m(cid:9)(cid:0)(cid:12)at(cid:8)(cid:12)(cid:0)Ð15¡C
e 0.06 P(cid:0)ak399nm
(cid:5)s
u
p
r
e
p 0.04
s
(cid:4)
(cid:2)o
o
(cid:3)
p
d 0.02
(cid:2)e
c
(cid:2)e
e
D 0.00
360 380 400 420 440
Wav(cid:0)l(cid:0)ngth(nm(cid:1)
Figure5: WavelengthspectrumoflightemittedforaDOMoperatingatamainboard(MB)temperatureof 15 C.The
− ◦
y-axisshowstheaveragenumberofphotonsdetectedperpulseoftheLEDlight.
of the DOMsare notcontrolledandare initiallyunknown. The orientationof each DOM,and
therefore the initial direction of emitted light from each LED, is determined to a precision of
about10 by flashing individualhorizontalLEDs and studying the light arrivaltime at the six
◦
surroundingstrings. Hereonereliesondirectlightfroman LEDfacingatargetarrivingsooner
thanscatteredlightfromonefacingaway.
3. Flasherdataset
The data set used in this paperincludes at least 250 flashes from each DOM on string 63.
DOMswereflashedat1.2Hzinasequence,usinga70nspulsewidthandmaximumbrightness.
ThesixhorizontalLEDsoneachflasherboardwereoperatedsimultaneously,creatingapattern
of light with approximate azimuthal symmetry around the flasher string. Flash sequences for
DOMsatdifferentdepthswereoverlappingbutweresufficientlydisplacedintimethatpulsesof
observedlightwereunambiguouslyassignedtoindividualflashers.
AsseeninFig.6,thereisasubstantialvariationamongthechargescollectedinDOMsatap-
proximatelythesamedepthastheemitteronthesixsurroundingstrings.Someofthevariationis
duetorelativedifferencesinlightyieldbetweenLEDs,andsomeisduetodifferencesindistance
to,anddepthof,thesixsurroundingstrings. Otherreasonsmayincludenon-homogeneityofthe
ice.
The pulses corresponding to the arriving photons were extracted from the digitized wave-
formsandbinnedin25nsbins,from0to5000nsfromthestartoftheflasherpulse(extracted
fromthespecial-purposeATWDchanneloftheflashingDOM).Toreducethecontributionfrom
saturatedDOMs(mostofwhichwereneartheflashingDOMonstring63)[6],andtominimize
the effects of the systematic uncertaintyin the simulated angular sensitivity modelof a DOM,
thephotondatacollectedonstring63werenotusedinthefit. ADOMbecomessaturatedwhen
itishitbysomanyphotonsthatthechargeinitsdigitizedoutputisnolongerproportionaltothe
numberofincidentphotons.
Theangularsensitivitymodelspecifiesafractionofphotonsthataredetectedatagivenangle
withrespecttothePMTaxis. ItaccountsforthenominalDOMsensitivitymeasuredinthelab,
modified by the scattering in the column of re-frozenice (see Fig. 7 and furtherdiscussion in
7
3
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10
0 10 20 30 40 50 60
DOM number on string 63
Figure6: ChargecollectedbyDOMsonthesixneareststrings(121.8 126.6maway,triangles)andsix
−
next-to-neareststrings(211.4 217.9maway,circles),observedwhenflashingatthesamepositiononstring
−
63.
section5). VariationsintheangularsensitivitymodelhavealargeimpactonthesimulatedDOM
responsetothephotonsarrivingalongthePMTaxis(straightintothePMTorintothebackofa
DOM),whiletheresponsetophotonsarrivingfromthesidesofthePMTismuchlessaffected.
4. Six-parametericemodel
This section overviews the ice parameterization introduced in [4], which in this paper is
referredto as the six-parameterice model. The ice is described by a table of depth-dependent
parametersb (400)anda (400)relatedtoscatteringandabsorptionatawavelengthof400nm,
e dust
bythe depth-dependentrelativetemperatureδτ, andbythesix globalparameters(measuredin
[4]): α, κ, A, B, D, and E, which are described below. The thickness of the ice layers was
somewhatarbitrarilychosento be10m. Thescatteringandabsorptioncoefficientsofeachice
layerare bestinterpretedasthe averageof theirtrue valuesoverthe thicknessof the ice layer.
Thechosenthicknessof10misthesameasthevaluechosenin[4]butsmallerthanthevertical
DOM spacingof17m. Due tosmalldepthoffsetsbetweentheDOMsondifferentstrings, we
retainatleast1receivingDOMperlayer.
Thegeometricalscatteringcoefficientbdeterminestheaveragedistancebetweensuccessive
scatters (as 1/b). It is often more convenientto quote the effective scattering coefficient, b =
e
8
b (1 cosθ ), where θ is the deflection angle at each scatter. The absorption coefficient a
· − h i
determinestheaveragedistancetraveledbyaphotonbeforeitisabsorbed(as1/a).
Thewavelengthdependenceofthescatteringandabsorptioncoefficientsisgivenbythefol-
lowingexpressions(forwavelengthλinnm). Thepowerlawdependenceispredictedbytheo-
reticalmodelsoflightscatteringindustyice. Thepowerlawdependenceonphotonwavelength
was verifiedin the AMANDAstudy, usinglightsourceswith severaldifferentfrequencies[4].
Theeffectivescatteringcoefficient,withtheglobalfitparameterα,is
λ α
b (λ)=b (400) − .
e e
·(cid:18)400(cid:19)
The totalabsorptioncoefficientisthe sum of two components,onedueto dustand theothera
temperaturedependentcomponentforpureice[4]:
λ κ
a(λ)=a (λ)+Ae B/λ (1+0.01 δτ), with a (λ)=a (400) − .
dust − dust dust
· · ·(cid:18)400(cid:19)
Theparameterδτaboveisthetemperaturedifferencerelativetothedepthof1730m(center
ofAMANDA):
δτ(d)=T(d) T(1730m).
−
ThetemperatureT(K)vs.depthd(m)isparameterizedin[8]as:
T =221.5 0.00045319 d+5.822 10 6 d2.
−
− · · ·
Thetworemainingglobalparameters, Dand E, weredefinedin[4]inarelationshipestab-
lishingacorrelationbetweenabsorptionandscattering: a (400) 400κ D b (400)+E,but
dust e
· ≈ ·
arenotusedinthispaper.
Thisworkpresentsthemeasurementofthevaluesofb (400)anda(400)basedondatataken
e
atawavelengthof400nmandreliesonthesix-parametericemodeldescribedabovetoextrap-
olatescatteringandabsorptionforwavelengthsotherthan400nm.
5. Simulation
Thedetectorresponsetoflashingeachofthe 60DOMsonstring 63generateda largedata
set that required very fast simulations such that many different sets of the coefficients b (400)
e
anda (400)couldbecomparedefficientlywiththedata. AprogramcalledPPC(photonprop-
dust
agationcode,seeAppendix A),waswrittenforthispurpose. PPCpropagatesphotonsthrough
icedescribedbyaselectedsetofparametervaluesfor b (400)anda (400)untiltheyreacha
e dust
DOMorareabsorbed.WhenusingPPC,nospecialweightingschemewasemployedexceptthat
thesphericalDOMswerescaledupinradiusbyafactorof5to16, dependingontherequired
timingprecision6,andthenumberofemittedphotonswasscaleddownbyafactorof52 to162,
correspondingtotheincreasedareaoftheDOM.
6 Special care was taken to minimize any bias onphoton arrival times byoversizing DOMs. First, weoversize
DOMsinthedirectionperpendiculartothephotondirection inordertoavoidanartificiallyreducedpropagationpath
beforereachingthereceiver. Still,intheworstcase,anincreaseinsizebyafactorof16abovetothenominalDOM
dimensionsmayintroduceamaximumbiasof(16 1) 16.51cm/22cm/ns=11.3nstowardsearlierarrivaltimes(for
− ·
aDOMwithradius 16.51cmandforspeedoflightiniceof22cm/ns). However, onaveragethis errorissmaller.
Anadditionalconsiderationistheoverestimatedlossofphotonsiftheywouldgetabsorbedwhenenteringanoversized
DOM.ThereforeweallowthephotonstocontinuepropagatingevenafterhittinganoversizedDOM.
9
1
sitivity10-1
n
e
s
e
v -2
ati10
el
r
IceCube "hole ice"
IceCube nominal
-3
10
-1 -0.8 -0.6 -0.4-0.2 -0 0.2 0.4 0.6 0.8 1
cos(h )
Figure7: Angularsensitivity ofanIceCubeDOMwhereηisthephotonarrivalanglewithrespecttothe
PMTaxis. Thenominalmodel,basedonalabmeasurement,isnormalizedto1.0atcosη = 1. Thearea
underbothcurvesisthesame.
16
0.12 14
0.1 ]m 12
nce0.08 er n 10
accepta00..0046 [hotons p 68
p 4
0.02 2
0 0
250 300 350 400 450 500 550 600 650 250 300 350 400 450 500 550 600 650
wavelength [ nm ] wavelength [ nm ]
Figure8:Left:opticalmoduleacceptance: fractionofphotonsarrivingfromadirectionparalleltothePMT
axis(atcosη = 1)thatarerecorded. Notethattheacceptance hereismeanttoincludetheglassandgel
transmission and the PMTquantum and collection efficiencies. Theacceptance is substantially lower at
thepeakthantheroughly20-25%quantumefficiencyofthePMTalonebecauseitisgivenwithrespectto
thephotonsincidentonacross-sectionofaDOM,whichislargerthanthatofaPMT.Right: numberof
Cherenkovphotonsemittedbyonemeterofthesimulated baremuontrack(i.e.,muonwithoutsecondary
cascades),convolvedwiththeopticalmoduleacceptance. Theintegralunderthecurveis2450photons.
The relative angular sensitivity of the IceCube DOM was modeled according to the “hole
ice”descriptionof[9],whichisshowninFig.7. The“holeice,”acolumnoficeapproximately
30cminradiusimmediatelysurroundingtheIceCubestring,isdescribedbytakingintoaccount
an increased amount of scattering (with effective scattering length of 50 cm) via an empirical
modificationtotheeffectiveangularsensitivitycurveofthereceivingDOM.
TheDOMacceptanceisdefinedasthefractionofphotonsincidentontothecross-sectionofa
DOMthatcauseasignalinthePMT.Thisfractionaccountsforthelossesduetotheglassandgel
transmission,andincludesPMTquantumandcollectionefficiencies.Itwascalculatedaccording
to[6]foraDOMofradius16.51cm. At400nmtheDOMacceptanceforthephotonsarriving
atthePMTalongitsaxisis13.15%. Thiscorrespondstothenominalangularsensitivitycurve
10