A comparison study of CORSIKA and COSMOS simulations for extensive air showers

0.23 MB·English

by  Soonyoung Roh

A comparison study of CORSIKA and COSMOS simulations for
extensive air showers
SoonyoungRoha,b,JiheeKima,DongsuRyua,∗,HyesungKangc,KatsuakiKasaharad,Eiji
Kidod,AkimichiTaketae
aDepartmentofAstronomyandSpaceScience,ChungnamNationalUniversity,Daejeon305-764,SouthKorea
3 bDepartmentofPhysics,GraduateSchoolofScience,NagoyaUniversity,Nagoya464-8602,Japan
1 cDepartmentofEarthSciences,PusanNationalUniversity,Pusan609-735,SouthKorea
0 dInstituteforCosmicRayResearch,UniversityofTokyo,Chiba277-8582,Japan
2 eCenterforHighEnergyGeophysicsResearch,EarthquakeResearchInstitute,UniversityofTokyo,Tokyo113-0032,
Japan
n
a
J

2
2
Abstract

]
E Cosmicrayswithenergyexceeding∼ 1018 eVarereferredtoasultra-highenergycosmicrays
H (UHECRs). Monte Carlo codes for extensive air shower (EAS) simulate the development of
. EASs initiated by UHECRs in the Earth’s atmosphere. Experiments to detect UHECRs uti-
h
lizeEASsimulationstoestimatetheirenergy,arrivaldirection,andcomposition. Inthispaper,
p
- we compare EAS simulations with two different codes, CORSIKA and COSMOS, presenting
o quantitiesincludingthelongitudinaldistributionofparticles,depthofshowermaximum,kinetic
r
t energy distribution of particle at the ground, and energy deposited to the air. We then discuss
s
implicationsofourresultstoUHECRexperiments.
a
[
Keywords: extensiveairshower,MonteCarlosimulation,ultra-highenergycosmicrays

1
v
0
6
0 1. Introduction
5
. Thenatureandoriginofultra-highenergycosmicrays(UHECRs)withenergyabove∼1018
1
eVareoutstandingproblemsofmodernphysics. Manystudieshavebeenperformedtounravel
0
3 the problems: where do UHECRs come from, what is the composition of UHECRs, and how
1 are UHECRs accelerated to such extreme energies? UHECRs are believed to be the result of
: extremely powerful cosmic phenomena [1]; the most powerful astrophysical events, such as
v
i activegalacticnuclei(AGNs)[2],gammaraybursts(GRBs)[3],andshockwavesaroundclusters
X
ofgalaxies[4],havebeensuggestedaspossiblesourcesofUHECRs. Yet,thenatureandorigin
r ofUHECRsremainunsolved(see[5,6]forreview).
a
Cosmicrays(CRs),whichareelectricallychargedparticles,donottravelinstraightlinesin
space. Theirtrajectoriesarebentbyintergalacticandinterstellarmagneticfieldsthatareknown
∗Correspondingauthor.
Emailaddresses:[email protected](SoonyoungRoh),[email protected](JiheeKim),
[email protected](DongsuRyu),[email protected](HyesungKang),
[email protected](KatsuakiKasahara),[email protected](EijiKido),
[email protected](AkimichiTaketa)
PreprintsubmittedtoAstroparticlePhysics January23,2013
to existbetweengalaxiesandbetweenstars[7, 8]. Forthisreason, eventhoughwe mayguess
theirarrivaldirectionsat the Earth, we do notknow exactly where theycome from. However,
thisproblemmayberesolvedifenougheventsofUHECRsareobserved.
Directly detecting UHECRs at the top of the Earth’s atmosphere is practically impossible
owing to the rarityof UHECR events. On average, only a few particleshit a square kilometer
oftheatmospherepercentury. SuchlowfluxofUHECRsdemandsexperimentscoveringhuge
areastoincreaseopportunitiesfortheirdetection. Inthe lastfewdecades,UHECRshavebeen
observedbyAkenoGiantAirShowerArray(AGASA)[9], HighResolutionFly’sEyeExperi-
ment(HiRes)[10],PierreAugerObservatory(AUGER)[11],TelescopeArray(TA)[12]andso
on. Theseexperimentsdetectextensiveairshowers(EASs)createdbyUHECRs.
WhenUHECRsentertheEarth’satmosphere,theyfirstcollidewithairmoleculesofoxygen
ornitrogen;subsequentlythroughcomplexinteractionsandcascades,EASs,whicharemadeof
uptohundredsofbillionsofsecondaryparticles(SeeTable1forthecaseof1019.5eVprimary),
are generated [13, 14]. By detecting the photons produced by secondary particles and/or the
secondaryparticlesarrivingattheground,thepropertiesofprimaryparticlessuchastheenergy,
arrivaldirection,andcompositionareinferred.
To observe UHECRs, AGASA used a ground array of scintillation detectors, HiRes used
fluorescence telescopes, AUGER uses a hybrid facility of water Cherenkov tanks and fluores-
cence telescopes, and TA also uses a hybrid facility of scintillation detectorsand fluorescence
telescopes. Fluorescencetelescopes measurethe ultra-violet(UV) fluorescencelightproduced
throughinteractionsbetweenairmoleculesandsecondaryparticlesinEASs,andarraysofscintil-
lationdetectorsandwaterCherenkovtanksrecodethesecondaryparticlesarrivingattheground.
Fromthese,AGASAreported58eventsabove40EeV[15].HiResobserved13eventsabove56
EeV[16]. AUGERandTAhavesofarreported69events[17]and15events[18]above55EeV
and57EeV,respectively.
Along with observationsof UHECRs, EASs need to be investigated by performingMonte
Carlo(MC)simulations. EASsimulationsformanessentialpartofUHECRexperiments. The
TA experimentemploys two existing MC codes for the simulations, CORSIKA (COsmic Ray
SImulationsforKAscade) [19] and COSMOS [20, 21]. In this paper, we reporta comparison
study ofCORSIKA andCOSMOS simulationsforTA, presentingthe longitudinaldistribution
ofparticle,depthofshowermaximum,kineticenergydistributionofparticleattheground,and
energydepositedtotheair. WethendiscussimplicationsofourresultstotheTAexperiment.
2. EASsimulation
CORSIKAandCOSMOSfollowthedevelopmentandevolutionofEASsintheatmosphere;
theydescribethespatial,temporal,andenergydistributionsofsecondaryparticles. Tocompare
CORSIKA and COSMOS, we generated 50 EAS simulations with CORSIKA for each set of
parameters(seebelow)andanother50EASsimulationswithCOSMOSforeachsetofparam-
eters. Primary energiesof E = 1018.5eV, 1018.75eV, 1019eV, 1019.25eV, 1019.5eV, 1019.75eV and
0
1020eVwereconsidered. Andzenithanglesofθ=0◦,18.2◦,25.8◦,31.75◦,45◦,70◦ forproton
andironprimarieswereemployedassumingthefatEarth. All togetherabout8,400EASswere
generated. Eventswith θ ≤45◦ havebeenanalyzedintheTAexperiment[18], sowefocuson
thecaseswithθ ≤45◦. Simulationswithθ=70◦ areusedtoestimatetheenergydepositedinto
the air in Section 3.4. Version 6.960 was used for CORSIKA simulations with θ = 0◦, 18.2◦,
25.8◦,31.75◦,and45◦,andversion6.980wasusedforθ=70◦. InCOSMOS,forθ=0◦,18.2◦,
25.8◦,31.75◦,and45◦,30simulationsweregeneratedwithversion7.54and20simulationswith
2
version7.581;thedifferencebetweenversions7.54and7.581issmall,sotheyweremixed. For
θ=70◦,version7.581wasused.
2.1. InteractionmodelsofCORSIKAandCOSMOS
Forhigh-energy(E > 80 GeV), the hadronicinteractiongeneratorQGSJETII-03[22] was
used forbothCORSIKA and COSMOS. QGSJETII-03is one of most widely used interaction
generatorsforUHECREASsimulations.
Forlow-energy(E < 80GeV),thehadronicinteractiongeneratorCORSIKA-FLUKA[23]
wasusedinCORSIKA,whiletheBertiniandJQMDinteractionmodelsincludedinthePHITS
code(E <2GeV)[24]andJAM(v1.150)(2GeV< E <80GeV)[25]wereusedinCOSMOS.
Wesimplyusetheterm“PHITS”forthetwogeneratorsandthenelstroutinemanagingtheelastic
scattering.
In CORSIKA, the interactions of electro-magnetic (EM) particles (i.e., photons and elec-
trons)werecalculatedwiththeEGS4model[26]. Ontheotherhand,inCOSMOS,theinterac-
tionswerecalculatedwiththeTsai’sformula[27]andNelson’sformula[26]whicharebasedon
thebasiccross-sectionsofparticles.
2.2. Simulationset-up
Weemployedthefollowingsimulationparameters,tryingto compareCORSIKAandCOS-
MOSsimulationsinparallel.First,inbothCORSIKAandCOSMOS,theEarth’smagneticfield
attheTAobservationsite(39.1◦Nand112.9◦W,justwestofDelta,Utah)wasused.Theground
was fixed at the heightof the TA site, 1430 m above the sea level, correspondingto the verti-
cal atmospheric depth x = 875 g/cm2. Second, in both CORSIKA and COSMOS, the same
v
thresholdenergies,E ,wereappliedtosecondaryparticles. Particleshavingenergybelow
threshold
E werenottrackedinsimulations. E =500keVwasusedforEMparticles,while
threshold threshold
E =50MeVformuonsandhadrons. Mostparticlesreachthegroundwithenergylarger
threshold
thanthe E (seeFigures4and5forthecaseofironprimarywith E = 1019.5eVandθ =
threshold 0
0◦).Third,theLandau-Pomeranchuk-Migdal(LPM)effect[28,29,30]isincludedinbothCOR-
SIKAandCOSMOS.TheLPMeffectcausesareductionofbremsstrahlungandpairproduction
crosssectionsathighenergies.
Inprinciple,allsecondaryparticlescanbetrackedalongtheirtrajectoriesandtheirphysical
propertiescanbestoreduntiltheyreachtheground. Then,thenumberofparticlescanbecome
toolargetobecomfortablyaccommodatedwithavailablecomputationalresources. Toalleviate
thisproblem,mostEASsimulationsintroducetheHillasthinningalgorithm[31].Thealgorithm
picks up only a small fraction for secondary particles with energy smaller than the productof
theprimaryenergy(E )andathinninglevel(L ),i.e.,forparticleswith E ≤ E ×L . Ateach
0 th 0 th
vertexofinteraction,onesecondaryparticleisselectedinawaythatmoreenergeticparticlesare
pickedupwithhigherprobabilities,andfurthertracked. A weight,whichisdefinedastheratio
oftheenergyoftheselectedparticletothatofallsecondaryparticlesatthevertex,isassignedto
theselectedparticletorepresentuntrackedparticles. Eventually,thetotalnumberofsecondary
particlesarerecoveredbycountingtrackedparticlesmultipliedbytheirweights[32].
InCORSIKA,itisrecommendedtotakeavaluebetween10−3 and10−7 for L . We chose
th
L = 10−7. Onthe otherhand,inCOSMOS, itisrecommendedto use L = A×10−7, where
th th
Aisthemassnumber. Hence,forprotonprimary, L = 1×10−7 wasusedforbothCORSIKA
th
andCOSMOS;forironprimary, L = 1×10−7 andL = 5.6×10−6 wereusedforCORSIKA
th th
andCOSMOS,respectively.Inaddition,COSMOSappliesasmallerthinning,L′ =10−2×L ,
th th
3
where a higher accuracy is required. At the upper atmosphere of x < 400 g/cm2 or near the
v
showercoreofr <20m,L isused,whileL′ isappliedtotheregionof x = 400−875g/cm2
th th v
andr≥20m.
CORSIKA and COSMOS both have an upperlimit on the weight, theso-called maximum
weightvalue, W . As anEASdevelops,throughinteractionsofparticles, weightsoftracked
max
particles are continuously accumulated. When accumulated weights reach W , the thinning
max
algorithmisnolongerapplied,andparticlesaretrackedwithoutfurtherthinning.WeusedW
max
which is differentlyfor CORSIKA and COSMOS: W = L ×(E [eV]/109) forCORSIKA
max th 0
[14]andW = E [eV]/1015forCOSMOS[20].
max 0
Withourchoicesofthinningandweighting,overallmoreparticlesaretrackedinCOSMOS
thaninCORSIKA.Thecomputationtimeisroughlyproportionaltothenumberoftrackedparti-
cles,soforthesameprimaryCOSMOSsimulationspresentedheretooklongerthanCORSIKA
simulations.
WealsonotethatthedatadumpingisdifferentbetweenCORSIKAandCOSMOS.InCOR-
SIKA, the grid points of the vertical atmosphericdepth have a spacing of ∆x = 1 g/cm2. On
v
the other hand, in COSMOS, the grid points are defined at x = 0, 100, 200 g/cm2, and after
v
200g/cm2theyhaveaspacingof∆x =25g/cm2. SothedatafromCORSIKAsimulationsare
v
dumpedinevery∆x =1g/cm2,whilethedatafromCOSMOSaredumpedinevery∆x =100
v v
g/cm2forx ≤200g/cm2andinevery∆x =25g/cm2forx >200g/cm2.
v v v
3. ComparisonofCORSIKAandCOSMOSsimulationresults
3.1. Longitudinaldistributionofparticles
When UHECRs strike the atmosphere, most of the particles initially generated are neutral
and charged-pions. Neutral-pions quickly decay into two photons. Charged-pions(positively
ornegativelycharged)survivelonger,andeithercollidewithotherparticlesordecaytomuons
and muonneutrinos. Those particles producethe so-called EM and hadronicshowers. In EM
showers, photons create electrons and positrons by pair-production, and in turn electrons and
positronscreatephotonsviabremsstrahlung,andsoon. EMshowerscontinueuntiltheaverage
energyperparticledropsto ∼80MeV.Belowthisenergy,thedominantenergylossmechanism
is ionization rather than bremsstrahlung. Then, EM particles are not efficiently producedany-
more,andEASsreachthemaximum(seethenextsubsection). Inhadronicshowers,muonsand
hadronsareproducedthroughhadronicinteractionsanddecays.Here,hadronsincludenucleons
(neutronsandprotons),pions,andkaons.
Thenumberof secondaryparticlescreatedbyEM andhadronic showersinitially increases
and then decreases, as an EAS developsthroughthe atmosphere. The distribution of particles
alongtheatmosphericdepthiscalledthelongitudinaldistribution[33,34]. Here,wefirstcom-
parethelongitudinaldistributionsfromCORSIKAandCOSMOSsimulations,andanalyzethe
differencesinphoton,electron,muon,andhadrondistributions.
Figures1and2showthetypicallongitudinaldistributionsasafunctionofslantatmospheric
depth,x = x /cosθ. Linesrepresentthenumbersofparticlesaveragedfor50EASsimulations,
s v
hNi,anderrorbarsmarkthestandarddeviations,σ,definedas
1 nsim
σ= (N −hNi)2. (1)
vtn i
sim Xi=1
4
Here, n = 50 is the number of EAS simulations for each set of parameters and N is the
sim i
numberofparticlesat x ineachsimulation.TheEASsshownareforprotonandironprimaries,
s
respectively,withE =1019.5eVandθ=0◦and45◦. Numbersforphotons,electrons,muons,and
0
hadronsareshown. Table1showsthenumbersofparticlesatpeaks,whichareagainaverages
of 50 EAS simulations. If the peaksare located beyondthe maximumdepth, the valuesat the
maximumdepthareshown.Notethatdifferencespecieshavepeaksatdifferentx ’s.
s
In the cases shown, COSMOS predicts slightly more particles in the early stage of EASs
(exceptforphotonsintheupper-leftpanelofFigure1),whileCORSIKApredictsslightlymore
particles in the late stage. But the difference is within the fluctuation (that is, less than σ in
Equation (1)). Quantitatively, the difference between CORSIKA and COSMOS results in the
peaknumbersofparticlesisatmost7−8%,asshowninTable1.
3.2. Depthofshowermaximum
Thedepthofshowermaximum,denotedby X , isdefinedastheslantatmosphericdepth
max
atwhichthenumberofsecondaryelectronsreachesthemaximuminEASs. X isa function
max
oftheprimaryenergy,butithasdifferentvaluesanddispersionsfordifferentprimaryparticles.
Foragivenprimaryenergy,protonprimaryhaslargervalues anddispersionsof X thaniron
max
primary. The average and standard deviation of X , hX i and σ , are known as the key
max max Xmax
quantitiesthatdiscriminatethecompositionofprimaryparticlesinUHECRexperiments.
IncalculatingX ,thelongitudinaldistributionofelectronsalongtheshoweraxiswasfitted
max
totheGaisser-Hillasfunction(GHF)[35],
Xmax−xs0
x −x λ X −x
N (x )= N s s0 exp max s , (2)
electron s electron,max Xmax−xs0! (cid:18) λ (cid:19)
where N isthemaximumnumberofelectronsat X . WesoughtX bytreating x
electron,max max max s0
andλaswellasX andN asfittingparameters.Wenotethatoriginallyx wasmeant
max electron,max s0
tobethedepthatwhichthefirstinteractionoccursand λtobetheprotoninteractionmeanfree
path. Butin practice,theywereregardedasfittingparameters. Itwasshownthatthe resulting
X isnotsensitivetowhetherλisusedasafreeparameterorsettoafixedvalue[36,37].
max
Figure3andTable2showhX iandσ inoursimulationsforprotonandironprimaries
max Xmax
with different E ’s. hX i and σ in Table 2 were calculated for250 simulationsincluding
0 max Xmax
those of fivedifferentzenithangles(θ ≤ 45◦). Solid anddashedlinesin Figure 3 arethe least
chi-squarefitsofhX iandσ inTable2. TheresultofWahlbergetal. withCORSIKA[38]
max Xmax
isincludedwithdot-dashedlinesforcomparison.
Wenotethatinsomesimulationstheshowermaximumoccurredbeyondthemaximumdepth.
In suchcases, X ’s fromfitsto the GHFmayhavelargererrors. AndforCORSIKA results,
max
thedatadumpedinevery∆x =1g/cm2wereused,whileforCOSMOSresults,thedatainevery
v
∆x =25g/cm2wereused.SoalargersystematicerrormayexistinCOSMOSresults.
v
The resultsfor hX i andσ in Figure3 and Table 2 are summarizedas follows. First,
max Xmax
the difference between CORSIKA and COSMOS results in hX i is at most ∼ 16 g/cm2 for
max
bothprotonandironprimaries. Itissmallerthanthefluctuation,σ . Second,thedifference
Xmax
between hX i’s forprotonand iron primariesis typically ∼ 70−80 g/cm2, which is beyond
max
thefluctuationsbothinCORSIKAandCOSMOSsimulationsaswellasthedifferencebetween
CORSIKAandCOSMOSresults.Third,σ is∼40−60g/cm2inforprotonprimary,whileitis
Xmax
∼20−25g/cm2forironprimary. σ issomewhatlargerinCORSIKAthaninCOSMOS,asis
Xmax
clearinFigure3;thedifferenceislargerforprotonprimary.Fourth,ourCORSIKAresultsagree
5
withthoseofWahlbergetal. Yetoursaresmallerbyupto ∼ 10g/cm2. Anumberofpossible
causes can be conjectured. Our simulations performedwith versions, models, and parameters
differentfrom those of Wahlberg et al. In ourwork hX i is defined as the depth of the peak
max
inthenumberofelectronsabove500keV,whileinWahlberget al. itwasdefinedasthedepth
ofthepeakinoverallenergydeposit. Alsotheerrorinthefittingcouldbein thelevelof∼ 10
g/cm2. Althoughnotshownhere,wefoundthathX ifordifferentzenithanglesvariesbyupto
max
∼10g/cm2.
3.3. Kineticenergydistributionofparticlesattheground
In EASs, a fractionof secondaryparticlesreachthe ground. Thoseparticlesdeposita part
oftheirenergytogrounddetectors,suchasscintillationdetectorsorwaterCherenkovtanks. In
experiments,bymeasuringtheamountandspatialdistributionofthedepositedenergy,thepri-
maryenergyandarrivaldirectionofUHECRsareestimated[39]. Here, wepresentthekinetic
energy(i.e.,thetotalenergysubtractedbytherest-massenergy)distributionsofsecondarypar-
ticles overtheentire ground;the amountofenergydepositedto detectorsisdeterminedbythe
kineticenergy.
Figure 4 shows the typical kinetic energy distributions of photons, electrons, muons, and
hadrons,includingparticlesintheshowercore;heretheEASisforironprimarywithE =1019.5
0
eVandθ = 0◦. Linesaretheaveragesof50EASsimulations,anderrorbars markthestandard
deviations, σ, definedsimilarlyas in Equation(1). Tables3, 4, 5, and 6show thetotalkinetic
energies(E)andnumbers(N)ofparticlesreachingthegroundforeachparticlespecies. Again,
theyaretheaveragesof50EASsimulations. Tofurtheranalyzethekineticenergydistributions
ofdifferentcomponents,hadronswereseparatedintonucleons,pions,andkaons,andFigure5
showstheirdistributions.
We first point that although N ≫ N ≫ N ≫ N for all the cases we
photon electron muon hadron
simulatedasshowninTables5and6, theenergypartitioningdependsonEASparametersand
variessignificantlyas shownin Tables3 and4. Forinstance, in the EASof ironprimarywith
E = 1019.5 eV and θ = 0◦ which is shown in Figures 4 and 5, the partitioning of the kinetic
0
energiesofparticlesreachingthegroundis E : E : E ∼1:0.18:0.11. Ontheother
EM muon hadron
hand,intheEASofprotonprimarywithE =1018.5eVandθ=45◦,E :E :E ∼1:
0 EM muon hadron
1.1:0.11.
WefoundthatthedifferencebetweenCORSIKAandCOSMOSresultsinFigures4and5is
up to 30%, butyetthe differenceis withinthe fluctuationat mostenergybins. Tables3, 4, 5,
and6 indicatedifferencesofupto 30%inthe integratedkineticenergiesandnumbers. There
arefollowinggeneraltends: 1)Formostcases, CORSIKApredictslargerenergiesforphotons
and electrons, while COSMOS predicts largerenergies for muons. 2) The difference is larger
forprotonprimarythanforironprimary. 3)Thedifferenceislargerforlarger E andforlarger
0
θ. Wenotethatlargernumbersofparticlesdonotnecessarily meanlargerenergies;thispointis
particularlyclearformuons.
3.4. Energydepositedtotheair
Interactions between air molecules and secondary particles yield UV fluorescence light,
which is observed with fluorescence telescopes in UHECR experiments [40, 41]. The energy
estimatedthroughobservationofUVfluorescencelightiscalledthecalorimetricenergy,andit
is used to inferthe primary energyof UHECRs [42]. The energy released as the fluorescence
lightisdeterminedbytheenergydepositedtotheair, E . Soinorderfortheprimaryenergyto
air
beaccuratelyestimatedinUHECRexperiments,E needstobepreciselyknown[43].
air
6
We compare the energy deposited to the air due to EM particles, muons, and hadrons in
CORSIKAandCOSMOSsimulations. BothCORSIKAandCOSMOSfollowE bytheparti-
air
cleswithE > E alongtheatmosphericdepthinsimulations. Butthecodesdoesnottrack
threshold
particlesandtheircontributionanymore, if theirenergydropsbelowthe thresholdenergy. So
we compare E byparticleswith E > E . Figure6shows E asa functionofthe slant
air threshold air
atmosphericdepth, x ,forprotonprimarywith E = 1019.5eVandθ = 0◦,31.75◦,45◦ and70◦.
s 0
Linesaretheaveragesof50EASsimulations. Table7showstheaverageofthefractionofthe
energy,hE i/E ,andtherelativestandarddeviation,σ /hE i,forprotonandironprimaries
air 0 Eair air
with different primary energies and θ = 70◦ at the ground; for θ = 70◦ the slant atmospheric
depth at the ground is large enough that E has reached the maximum (see Figure 6). The
air
valuesinTable7werecalculatedwith50EASsimulationsforeachsetofparameters.
ThereisacleartrendinFigure6thatCOSMOSpredictslarger E (x )thanCORSIKA.The
air s
energydepositedtotheairbytheparticleswithE > E inTable7ishE i/E =0.66−0.71
threshold air 0
inCORSIKAsimulations,whilehE i/E =0.77−0.82inCOSMOSsimulations.Thedifference
air 0
is ∼ 15 %, which is largerthan the fluctuation. The relative standard deviation, σ /hE i, is
Eair air
smallandtypically∼1%bothinCORSIKAandCOSMOSsimulations.
For the total energy deposited to the air, the contribution due to the particles with E <
E ,aswellasthatbytheparticleswithE > E ,shouldbecounted.Yet,thedifference
threshold threshold
of∼ 15%issubstantial. ItmeansthattheUVfluorescencelightassessedwithCORSIKAand
COSMOSsimulationscoulddifferbyasimilaramount,sodoestheprimaryenergyofUHECR
eventsestimatedwithCORSIKAandCOSMOSsimulations.
4. Summary
EASsimulationsformanessentialpartofexperimentstodetectUHECRs; theyareusedto
estimatetheenergy,arrivaldirection,andcompositionof primaryparticles. TheTAexperiment
employstwocodes,CORSIKAandCOSMOS,forthesimulations. Inthispaper,wecompared
CORSIKAandCOSMOSsimulationsbyquantifyingthedifferencesinthelongitudinaldistribu-
tionofparticles,depthofshowermaximum,kineticenergydistributionofparticleattheground,
andenergydepositedtotheair.
Mostof all, we shouldpointthatthe simulation resultsof CORSIKA andCOSMOS agree
wellwitheachother,despiteofallthecomplexitiesanddifferencesinthemodelsandelements
involvedinthecodes. Suchagreementshouldbequiteanachievement. Nevertheless,thereare
non-negligibledifferencesinthequantitieswepresented. Thosemayberegardedassystematic
uncertaintiesintheEASsimulationpartofUHECRexperiments.
1)ThedifferencebetweenCORSIKAandCOSMOSresultsinthelongitudinaldistributionof
particlesislessthan∼10%formostcases,whichiswithinthefluctuation.Thedifferenceinthe
peaknumbersofparticlesisatmost7−8%(Table1). COSMOStendstopredictslightlymore
particlesintheearlystageofEASs,whileCORSIKAtendstopredictslightlymoreparticlesin
thelatestage.
2)CORSIKAandCOSMOSpredictthedepthsofshowermaximum,hX i,whicharecon-
max
sistent with each other. The differencebetween hX i’s fromCORSIKA and COSMOS is up
max
to ∼ 16 g/cm2, which is noticeable but smaller than the fluctuation, σ . The difference be-
Xmax
tweenhX i’sforprotonandironprimaries,whichistypically ∼ 70−80g/cm2,isbeyondthe
max
fluctuationsbothinCORSIKAandCOSMOSsimulationsaswellasthedifferencebetweenthe
CORSIKA and COSMOS results. σ is ∼ 40−60 g/cm2 in for proton primary, while it is
Xmax
7
∼20−25g/cm2forironprimary. σ issomewhatlargerinCORSIKAthaninCOSMOS;the
Xmax
differenceislargerforironprimary.
3) There are differences of up to 30 % between CORSIKA and COSMOS results in the
numbers and energies of the particles reaching the ground; the difference is larger for proton
primary with larger E ’s and larger θ’s. It implies that the amount of the energy deposited to
0
grounddetectorscouldbe differentupto30%orso inCORSIKA andCOSMOS simulations.
The exactresponseto the particlespassing throughgrounddetectors, however,dependsonthe
details of detectors, and need simulations, for instance, with the GEANT code. We leave this
issueforafollow-upstudy.
4)Theenergydepositedtotheair,E ,bytheparticleswithE >E islargerby∼15%
air threshold
inCOSMOSsimulationsthaninCORSIKAsimulations. ThisimpliesthattheUVfluorescence
lightassessedwithCORSIKAandCOSMOSsimulationscoulddifferbyasimilaramount.
Acknowledgments
We thanktherefereeforcriticalreadingofthemanuscriptandconstructivecomments. We
thanks the CORSIKA user supportteam for help in using CORSIKA. KK thanks K. Niita for
courtesy and help in implementing the PHITS code. The work of SR, JK, DR, and HK was
supported by the National Research Foundation of Korea through grant 2007-0093860. The
work of KK, EK, and AT was supported by Grant-in-Aid for Scientific Research on Priority
Areas(HighestEnergyCosmicRays: 15077205).
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0 degree 45 degree
1.5•1011
1.0•1011
>
Nphoton
< 5.0•1010
0

2.0•1010
N>electron 11..05••11001100
<
5.0•109
0

1.5•108
>
muon 1.0•108
N
<
5.0•107
0

CORSIKA
8•107 COSMOS
N>hadron 46••110077
<
2•107
0
0 200 400 600 800 200 400 600 800 1000 1200
Atmospheric slant depth [g/cm2]
Figure1: Longitudinaldistributionofphotons,electrons, muons,andhadronsforEASsofprotonprimarywith E0 =
1019.5eVandθ=0◦(leftpanels)and45◦(rightpanels). Linesrepresenttheaveragesof50simulations,anderrorbars
markthestandarddeviations.Forclarity,onlytheerrorbarsofCORSIKAresultsareshown.
10