A comparison of the cosmic-ray energy scales of Tunka-133 and KASCADE-Grande via their radio extensions Tunka-Rex and LOPES

2016

Publication Year

2020-06-03T13:27:32Z

Acceptance in OA@INAF

A comparison of the cosmic-ray energy scales of Tunka-133 and

KASCADE-Grande via their radio extensions Tunka-Rex and LOPES

Title

Apel, W. D.; Arteaga-Velázquez, J. C.; Bähren, L.; Bezyazeekov, P. A.; Bekk, K.; et

al.

Authors

10.1016/j.physletb.2016.10.031

DOI

http://hdl.handle.net/20.500.12386/25901

Handle

PHYSICS LETTERS. SECTION B

Journal

763

Number

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

A

comparison

of

the

cosmic-ray

energy

scales

of

Tunka-133

and

KASCADE-Grande

via

their

radio

extensions

Tunka-Rex

and

LOPES

Tunka-Rex

and

LOPES

Collaborations

W.D. Apel

a

,

J.C. Arteaga-Velázquez

b

,

L. Bähren

c

,

P.A. Bezyazeekov

d

,

K. Bekk

a

,

M. Bertaina

e

,

P.L. Biermann

f

,

J. Blümer

a

,

g

,

H. Bozdog

a

,

I.M. Brancus

h

,

N.M. Budnev

d

,

E. Cantoni

e

,

i

,

A. Chiavassa

e

,

K. Daumiller

a

,

V. de Souza

j

,

F. Di Pierro

e

,

P. Doll

a

,

R. Engel

a

,

H. Falcke

c

,

f

,

k

_,

_{O. Fedorov}

d

_,

_{B. Fuchs}

g

_,

_{H. Gemmeke}

l

_,

_{O.A. Gress}

d

_,

_{C. Grupen}

m

_,

_{A. Haungs}

a

_,

D. Heck

a

,

R. Hiller

a

,

∗

,

J.R. Hörandel

k

,

A. Horneffer

f

,

D. Huber

g

,

T. Huege

a

,

P.G. Isar

n

,

K.-H. Kampert

o

,

D. Kang

g

,

Y. Kazarina

d

,

M. Kleifges

l

,

E.E. Korosteleva

p

,

D. Kostunin

a

,

O. Krömer

l

,

J. Kuijpers

k

,

L.A. Kuzmichev

p

,

K. Link

g

,

N. Lubsandorzhiev

p

,

P. Łuczak

q

,

M. Ludwig

g

,

H.J. Mathes

a

,

M. Melissas

g

,

R.R. Mirgazov

d

,

R. Monkhoev

d

,

C. Morello

i

,

J. Oehlschläger

a

,

E.A. Osipova

p

,

A. Pakhorukov

d

,

N. Palmieri

g

,

L. Pankov

d

,

T. Pierog

a

,

V.V. Prosin

p

,

J. Rautenberg

o

,

H. Rebel

a

,

M. Roth

a

,

G.I. Rubtsov

r

,

C. Rühle

l

,

A. Saftoiu

h

,

H. Schieler

a

,

A. Schmidt

l

,

S. Schoo

a

,

F.G. Schröder

a

,

O. Sima

s

,

G. Toma

h

,

G.C. Trinchero

i

,

A. Weindl

a

,

R. Wischnewski

t

,

J. Wochele

a

,

J. Zabierowski

q

,

A. Zagorodnikov

d

,

J.A. Zensus

f

a_{InstitutfürKernphysik,KarlsruheInstituteofTechnology(KIT),Karlsruhe,Germany} b_{InstitutodeFísicayMatemáticas,UniversidadMichoacana,Morelia,Michoacán,Mexico} c_{ASTRON,Dwingeloo,TheNetherlands}

d_{InstituteofAppliedPhysicsISU,Irkutsk,Russia}

e_{DipartimentodiFisica,UniversitàdegliStudidiTorino,Torino,Italy} f_{Max-Planck-InstitutfürRadioastronomie,Bonn,Germany}

g_{InstitutfürExperimentelleKernphysik,KarlsruheInstituteofTechnology(KIT),Karlsruhe,Germany} h_{NationalInstituteofPhysicsandNuclearEngineering,Bucharest-Magurele,Romania}

i_{OsservatorioAstrofisicodiTorino,INAFTorino,Torino,Italy}

j_{InstitutodeFísicadeSãoCarlos,UniversidadedeSãoPaulo,SãoCarlos,Brazil}

k_{DepartmentofAstrophysics,RadboudUniversityNijmegen,AJNijmegen,TheNetherlands}

l_{InstitutfürProzessdatenverarbeitungundElektronik,KarlsruheInstituteofTechnology(KIT),Karlsruhe,Germany} m_{FacultyofNaturalSciencesandEngineering,UniversitätSiegen,Siegen,Germany}

n_{InstituteforSpaceSciences,Bucharest-Magurele,Romania}

o_{FachbereichC,Physik,BergischeUniversitätWuppertal,Wuppertal,Germany} p_{SkobeltsynInstituteofNuclearPhysicsMSU,Moscow,Russia}

q_{DepartmentofAstrophysics,NationalCentreforNuclearResearch,Łód´z,Poland} r_{InstituteforNuclearResearchoftheRussianAcademyofSciences,Moscow,Russia} s_{DepartmentofPhysics,UniversityofBucharest,Bucharest,Romania}

t_{DESY,Zeuthen,Germany}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received6June2016

Receivedinrevisedform27September 2016

Accepted13October2016 Availableonline18October2016 Editor:S.Dodelson

Theradiotechniqueisapromisingmethodfordetectionofcosmic-rayairshowersofenergiesaround 100PeV andhigherwithanarrayofradioantennas.Sincetheamplitudeoftheradiosignalcanbe mea-suredabsolutelyand increaseswiththeshowerenergy,radiomeasurementscanbeused todetermine theair-shower energyonanabsolutescale.Weshow thatcalibratedmeasurements ofradiodetectors operated incoincidencewithhost experimentsmeasuring airshowers basedonothertechniques can be used for comparing the energyscales ofthese host experiments. Using two approaches,first via

*

Correspondingauthor.

E-mailaddress:roman.hiller@kit.edu(R. Hiller).

http://dx.doi.org/10.1016/j.physletb.2016.10.031

0370-2693/©2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

180 Tunka-Rex and LOPES Collaborations / Physics Letters B 763 (2016) 179–185 Keywords: Cosmicrays Radiodetection LOPES Tunka-Rex Tunka-133 KASCADE-Grande

direct amplitude measurements, and secondviacomparison of measurements withair shower simu-lations,wecomparetheenergyscalesoftheair-showerexperimentsTunka-133andKASCADE-Grande, usingtheirradioextensions, Tunka-RexandLOPES, respectively.Duetothe consistentamplitude cali-brationforTunka-RexandLOPESachievedbyusingthesamereferencesource,thiscomparisonreaches anaccuracyofapproximately10% –limitedbysomeshortcomingsofLOPES,whichwasaprototype ex-perimentforthedigitalradiotechniqueforairshowers.Inparticularweshowthattheenergyscalesof cosmic-raymeasurementsbytheindependentlycalibratedexperimentsKASCADE-GrandeandTunka-133 areconsistentwitheachotheronthislevel.

©2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Cosmic rays are charged, high-energy particles from space whichofferawindowtothemostenergeticprocessesinthe uni-verse. Their origin remains uncertain, as they are deflected by magnetic fields during propagation and thus do not point back totheirsources.Instead,sourcesorsourcepopulationshavetobe identified indirectly by comparing the measured flux per energy and the mass composition to model predictions [1]. The flux of cosmic-rayparticlesathighenergies,above1015eV,istoolowfor directmeasurements,butinsteadhastobereconstructedfromair showers, induced in the Earth’s atmosphere, measured with ex-tendeddevicesonground.Ascosmic-rayobservablesliketheflux ormass composition are always interpreted asa function of en-ergy,apreciseandaccurateenergymeasurementisofimportance toallcosmic-raydetectors.

Therearedifferentmethodsfordetectingairshowers,ofwhich mostcanbeclassifiedinparticledetectorarraysandoptical tech-niques.Particle detectorarraysmeasuringthe secondaryparticles at the observation level can be operated around-the-clock, and thusofferthehighestexposureandbesteventstatistics.Butthey are limited by systematic uncertainties from air-shower simula-tions based on hadronic interaction models beyond the energy range probed by accelerators, which are required for proper in-terpretation of thedata. Especiallythe muonic componentof air showers seems to be poorly described by contemporary models [2,3],possiblyalsodistortingtheenergyscaleofthedetectors. Op-ticaltechniques,detectingthe air-Cherenkov orfluorescencelight oftheelectromagneticair-showercomponentsufferlessfrom sys-tematicuncertainties ofair-shower simulations, butcan only op-erate during clearand dark nights, reducing the statistics by an order of magnitude. To overcome these problems, contemporary observatories combineadvantages from the different observation techniquesinhybriddetectors[4,5].

Theradiodetectiontechnique isapromisingdetectionmethod forhigh-energyairshowers,whichexperiencedarenewedburstof interestinthe2000s[6,7].Mainlyduetogeomagneticdeflectionof thechargedparticlesintheairshower,andtoalowerextentalso dueto a time-varyingcharge excess inthe shower front,a radio signal in the MHz range is emitted [8,9]. Due to the special co-herenceconditionsattheCherenkovanglethe emissionby these mechanismsextentseven uptothe GHzrangeatthisangle.This has been confirmed by recent measurements indicating that the radio emissionis beamedin theforwarddirectionof theshower notonlyatMHz,butalsoGHzfrequencies[10].Above1017_{eV the}

radiosignal atMHzfrequencies canbe detectedwithan array of radio antennas.With a full duty cycleandcompetitive precision, theradiodetectiontechnique combinesadvantagesofvarious ex-istingtechniques.Itslowdependenceondetailsoftheatmospheric conditions andon the muon content ofthe air shower makes it particularly suitable for an accurate measurement of the shower energy,whichforahybriddetectorisalreadypossiblewithavery sparsearray[11].

The energy measurement via the radio signal is connected to its amplitude scale,i.e., the strength ofthe electricfield emitted by theshower, asdemonstrated by several experiments [12–15]. In particular the possibility to measure the radio amplitude on an absolutely calibrated scale [16–19], thus enables an absolute measurementoftheshowerenergy.Asthepresentradiodetectors are mainlyoperatedtogetherwithhostdetectors,alsotheenergy scales oftheir hosts can becompared to eachother via the cali-bratedradiomeasurements.Inthispaperwepresenttwomethods to perform exemplarily such a comparison: first via the energy estimator of the radio detectors and, second, via comparison to CoREASsimulationsoftheradioemissionfromairshowers.Using thesemethods,theenergyscalesofthenon-imagingair-Cherenkov array Tunka-133 [20] and the particle-detector array KASCADE-Grande [21] are compared to each other, or more precisely the scale of the cosmic-ray energy spectra measured by these ex-periments around an energy of 1017_{eV of the primary particles.}

Tunka-133andKASCADE-Grandearehoststotheradioextensions Tunka-Rex [17] and LOPES [22], respectively. For Tunka-Rex and LOPESthecomparisonisespeciallyaccurateandstraightforward in interpretation,becausebothexperimentswerecalibratedwiththe same referencesource[23]. However,there arealso some limita-tions, sinceLOPES wasa prototypeexperimentinthenoisy envi-ronmentofaresearchcenter,sinceitcoveredonlyasmallpartof theKASCADE-Grande area,andsince itsantennamodelhassome shortcomings. This analysis sheds light on the systematic effects originating fromthe independentenergy calibrations ofboth ex-periments and thus facilitates a combined interpretation of data frombothexperiments.

2. Calibration

Theabsolutescalesoftheradioamplitudemeasuredby Tunka-RexandLOPEShavebeendefinedbyacalibrationwithareference source.DescriptionsoftheexactprocesscanbefoundinRefs.[17] and [16,23], respectively. Both experiments used the same refer-encesource.Therefore,thedominatinguncertaintyofthe calibra-tion, the amplitude scale of the reference source itself, cancels out whencomparing bothexperiments.Theremaining uncertain-ties of the amplitude scale that donot cancelout over multiple events and different antennas, are 6% from the temperature de-pendence ofthereferencesourceand3% fromsource positioning and alignment [17]. Moreover, there are uncertainties of several percent due to the dependence of the LOPES antenna gain on varying ground conditions[16],but thenet effect issmall, since the presentanalysis averages over many events recorded during different groundconditions.Simulations are usedto describe the angular dependence of the antenna response, which have short-comingsinthedescriptionofthezenithdependenceoftheLOPES antenna gain [24]. Unfortunately, a more accurate calibration of the zenithdependenceis notpossible, becauseLOPES is disman-tled since 2012. In summary, we estimate the uncertainty from theantennacalibrationto7% fortheamplitudescaleofTunka-Rex

andLOPES relative to each other, withan additional uncertainty oftheorderof10% fromthezenithdependenceoftheLOPES an-tenna model.The calibrationuncertainty constitutes a correlated systematicuncertaintyforthetwomethodsofcomparingthe en-ergyscalesintroducedinthenextsections.

TheenergycalibrationsofTunka-133andKASCADE-Grandeare both performed with the help of air shower simulations. The Tunka-133 calibration is based on the QUEST experiment which measured air-Cherenkov light of air showers coincidentally with theparticle-detector arrayEAS-TOP [25,26],whichitselfwas cali-bratedwithCORSIKAsimulationsusingdifferenthadronic interac-tionmodels,amongthemQGSJET[27,28].KASCADE-Grandeis cal-ibratedwitha newerversion CORSIKAusing differentinteraction models.Forthepurposeofthiscomparisonthe calibrationbased onQGSJET IIisused,sincethiswasusedforpreviously published results [23,29]. Despite some known deficits [3,30], QGSJET II is still one of the best hadronic models for air-shower simulations andwidelyused.

3. Comparisonoftheenergyscalesviaaradioenergyestimator

The energy scales of the host experiments can be compared directly via the measurement of the absoluteamplitude scale of theradiosignal inconjunctionwithshowerenergyreconstructed by the host experiment. This can be done with any of the en-ergyestimators typically used forradio detection ofair showers, andforthis analysiswe have chosen the amplitude ata charac-teristicdistancefromtheshoweraxis,sincethishasalreadybeen usedby both,LOPES andTunka-Rex, asenergyestimator[12,14]. TheLOPES experimentusedtheamplitudeoftheradio signalata distanceof100m. Thisdistancehasbeentuned tomaximize the precisionoftheenergyreconstructionforatypicaleventselection ofLOPES.Theamplitudeatthisdistancefeatureslittledependence onthedistancetotheshowermaximum,i.e.,littledependenceon thezenithangleandtheatmosphericdepth oftheshower maxi-mumofanairshower.Therefore,theamplitudeatthisdistanceis alsoa goodchoiceforthecomparisonto anotherexperimentlike Tunka-Rex.

ForLOPES the events used in this paper were acquired from theendof2005totheendof2009,andtriggeredbytheKASCADE particledetectorarray.Only eventswithan energyreconstructed byKASCADE-Grandeabove1017eV,azenithanglebelow40◦,and ashowercoreinsidethefiducialareaofKASCADEareused(likein Ref.[12]).Additionally eventsdisturbedby nearbythunderstorms areexcluded[31].Theresultingeventsareanalyzedwiththe stan-dardanalysispipelineofLOPESapplyingcertain qualitycuts, e.g., requiring a minimum signal-to-noise ratio (see Ref. [32] for de-tails),and178eventspassallqualitycriteria.Toallowforsufficient eventstatisticsintheradio-loudenvironmentoftheLOPES exper-iment,thissignal-to-noise criterion islessstrict thanthe onefor Tunka-Rex,whichimplieslargerper-eventuncertaintiesforLOPES. Thereconstructedsignal ofLOPES islimitedtotheeffectiveband of43 to74MHz,andonlythesignalintheeast–westaligned an-tenna was evaluated. A simple exponential function was used to determinetheradioamplitudeat100m distancefromtheshower axis, since the average effect of more subtle features of the ra-dio footprint (e.g., its east–west asymmetry and a bump at the Cherenkovangle)isonlyafewpercentforthisdatasetatthis dis-tance[32].Finally,theamplitudeat100m wasdividedbythesine ofthe geomagnetic anglein orderto normalize forthe direction dependenceofthestrengthofthegeomagneticradioemission.

Thisnormalizedamplitudeisproportionaltotheenergyofthe airshowerdeterminedbythehostexperimentwithamedian sig-nalamplitude per energy ofkLOPES

100

=

724

±

12μ V/m

EeV . The median

is usedhereto reduce theimpact ofsingle outlier eventsof un-knownoriginalreadyseeninearlierLOPESanalyses.Toaccountfor thedifferenceingeomagneticfieldbetweentheLOPESandTunka sites,weassumethattheamplitude oftheradio signalis propor-tionaltothemagneticfieldstrength,anddividekLOPES₁₀₀ bythevalue attheLOPESsiteof47 μT:

κ

LOPES

=

15

.

40

±

0

.

26_μμ_{T EeV}V/m.The

approx-imateproportionalityoftheradioamplitudewiththegeomagnetic Lorentz forcehasbeenconfirmedbymanyexperiments[6,7]. Re-cently,slightdeviationsfromanexactlyproportional scalingwith the magnetic field strength have been discussed based on sim-ulations [33]. If true, this would change our result for the ratio

κ

TRex

/

κ

LOPES by about 2%, andconsequently is negligible against

otheruncertainties.

A corresponding analysis has been performed for Tunka-Rex measurements withaneventselection followingthestandard re-construction methoddescribed inRef. [14]. Withthe used selec-tion criteria, both experiments have an energy thresholdaround 1017eV. Though the radio detection is not fully efficient at this threshold, the triggering host detectors are. Because of the low duty cycleoftheair-Cherenkov array Tunka-133,andthe shorter run time of Tunka-Rex compared to LOPES, the available event statisticsissimilarforbothexperiments,althoughTunka-Rex cov-ersamuchlargerarea.

ForTunka-Rex,theselectionyields196Tunka-133 eventsfrom October 2012 until April 2014 with energies above 1016.5_eV,

zenith angles

θ

≤

50◦, and successful reconstruction of the ra-dio signal. This implies the application of standard quality cuts used in other Tunka-Rex analyses (see Refs. [17,14]), in particu-lar a certain signal-to-noise ratio in at least three antennas and an agreement ofthearrival directionsreconstructed by theradio and the air-Cherenkov arrays. As only difference to the standard Tunka-Rexpipelinethefrequencyrangehasbeendigitallylimited to 43 to 74MHz after inverting the hardware response, i.e., the Tunka-Rex data have been evaluated inside the smaller effective bandofLOPES,insteadoftheusualeffectivebandof35 to76MHz ofTunka-Rex.

Fromtheresultingeventselection thereconstructedeast–west componentnormalizedto thesine ofthe geomagnetic anglewas evaluated. AsfortheLOPES analysis,the amplitudeat 100m dis-tance fromthe shower axishas beendetermined using a simple exponentialfunction foritslateraldistribution.Thecorrection for the small azimuthal asymmetry of the footprint, usually applied forTunka-Rex [34],was omittedhereasitisalsonot appliedfor LOPES, andsince ithasbeenshowntohavenegligibleimpacton statistical analyses averaging over many events [32]. The result-ing plotsof amplitudeversus the energydetermined bythe host experimentsareshowninFig. 1.Themedianoftheobtained am-plitude per energyiskTRex

100

=

879

±

11μ V/m

EeV forTunka-Rex which

afternormalizingtothemagneticfieldstrengthof60 μTresultsin

κ

TRex

=

14

.

65

±

0

.

18_μμ_{T EeV}V/m.

Inordertocomparetheobtainedvaluestoeachother,the dif-ference in observation level between Tunka-Rex and LOPES has to betakenintoaccount. The radioemission isgeneratedmainly aroundtheshowermaximum,whichintheobservedenergyrange typicallyisathigheraltitudesthantheobservationlevelsofboth experiments. Thus, the main effect is that the radio emission is spread over a larger area for deeper observation levels reducing theamplitude atagivendistancetotheshower axis.Thismeans that even atthe chosen characteristicdistance of100m the am-plitude dependsslightlyon thedistancefromthedetectorto the showermaximum,whichitselfdependsonthealtitudeofthe de-tector andforeach individual eventontheatmosphericdepth of theshowermaximumandonthezenithangle.Sincetheeffectof shower-to-shower fluctuationsof the depth ofshower maximum

182 Tunka-Rex and LOPES Collaborations / Physics Letters B 763 (2016) 179–185

Fig. 1. Amplitudeat100m measuredbytheradioarraysTunka-Rex(left)andLOPES(right)versustheshowerenergyreconstructedbytheirhostexperimentsTunka-133 andKASCADE-Grande,respectively,afterdivisionbythesineofthegeomagneticangle.Thelineindicatesthemedianoftheamplitudeperenergy,whichisusedtocompare theamplitudescalestoeachother.

Fig. 2. Amplitudeperenergyoftheeast–westcomponentofTunka-RexandLOPES versuszenithangle.Withtheindicatedzenithanglescorrespondingtotheaverage observationdepths, thesystematicuncertaintyduetothe differencein observa-tiondepthisestimated.ThereasonfortheoverallshiftbetweentheTunka-Rexand LOPESdataisthedifferentgeomagneticfieldstrengthandenergyscaleofthehost experiments.ThereasonforthedifferenttrendintheLOPESdatalikelyisthe defi-cientantennamodelappliedtotheLOPESmeasurements.

averageout over theevent statistics,only thezenithangle effect andthealtitudeofthedetectorsplayarolehere.

The LOPES event distribution has an average zenith angle of 27◦. Due to the higher observation altitude of Tunka-Rex, air showerswith27◦ zenithangle measured withTunka-Rex would, however, have a smaller distance to the shower maximum than at LOPES andconsequently a steeper footprint. Instead, showers with35◦ zenithangleatTunka-Rexhaveaboutthesamedistance to the shower maximum and are expectedto havea similar ra-diosignalonground.Thisangleisbychanceclosetotheaverage zenith angleof the Tunka-Rex event distribution of 41◦.The re-mainingsystematiceffectinthepresentanalysiscanbeestimated by the average difference in amplitude at the characteristic dis-tance of 100m between 35◦ and 41◦ zenith angle. As shown in Fig. 2, the resultingsystematicuncertainty on thecomparison of

κ

TRex and

κ

LOPES isapproximately7%,whichisaboutthesameas

thesystematicuncertaintyfromthecalibrationoftheexperiments. In principle the effect can be corrected. However, this makes onlysenseifallother systematiceffectsregardingtheshower in-clinationareunderstoodsufficientlywell,e.g.,aslightdependence oftheenergyscaleofthehostexperimentsontheshower inclina-tion.In our casethe dominatingsystematic uncertaintyof about 10% results from the deficient description of the zenith depen-denceofthe LOPES antennagain, whichlikely iswhythe LOPES data show a differenttrend over zenith angle. Consequently, we takethesizeoftheeffectobservedintheTunkadataasa method-specificsystematicuncertaintyof7%,andadditionally,10% uncer-taintyoftheLOPESantennamodelforallmethodsinthe interpre-tationofourresultsintheConclusion,Sec.5.

Since the measured energy Em from either experiment may

haveasystematicshiftcomparedtotherealenergyEreal,the

mea-suredcoefficient

κ

m deviatesfromtherealone

κ

real

κ

m

=

Ereal

Em

·

κ

real (1)

Thus, the energyscales of Tunka-Rex andLOPES andtheir hosts, KASCADE-Grande andTunka-133,can be comparedto eachother usingtheradiomeasurementsof

κ

m

famp

=

EKG ET133

=

κ

TRex

κ

LOPES

.

(2)

Theresultingratioofreconstructedenergiesis famp

=

0

.

95

±

0

.

07

for this method of comparing radio amplitudes, i.e., the energy scale ofKASCADE-Grande is

(

5

±

7

)

% lower thantheenergyscale ofTunka-133.Thisuncertaintyincludesonlymethod-specific con-tributions, which are dominated by the systematic effect due to thedifferenceinobservationdepth.

4. ComparisonoftheenergyscalesviaCoREASsimulations

AnotherwaytocompareLOPEStoTunka-Rexisbyusing simu-lationsoftheradioemissionfromairshowersasabenchmark,as longasthesamesimulationcodeisused.Byconfiguringthe sim-ulationsaccordingtotherespectivesitethedifferenceinmagnetic field andobservationdepthisautomaticallytakenintoaccountin this case. Forthe presentanalysis we used the CoREAS [35] ra-dio extension ofthe CORSIKAsimulationprogram forairshowers and the hadronic interaction model QGSJET in the versions II.03 for LOPES and II.04for Tunka-Rex, where both versions have al-mostnegligibledifferencefortheradioemission.Sincethetypeof primaryparticleaprioriisunknown,foreachmeasuredeventtwo simulationshavebeenperformed,oneeachfortheextremecaseof a protonandaniron nucleusasprimaryparticle.Theenergyand arrivaldirectionaresettothevaluesreconstructedbythehost ex-periments KASCADE-Grande andTunka-133, respectively, i.e., the energyscaleofthehostexperimentsisinputtothesimulations.

ForLOPES we used theCoREAS simulations alreadypresented in Refs. [32,23], and applied two additional improvements com-pared to these references, which make the comparison slightly more accurate (the effect is only a few percent and unim-portant for the previous analyses compared to their systematic uncertainties). First, since the energy calibration of KASCADE-Grandewasslightlyimprovedovertime,thesimulatedamplitudes were rescaled linearly accordingto the energyshiftbetween the KASCADE-Grande calibration used for production of the simula-tions andtheoneofRef. [29]usedinthispaper.Second,wenow

Fig. 3. RadioamplitudeateachTunka-Rexstationwithsignal(left),andat100m distancefromtheshoweraxisforeventsmeasuredbyLOPES(right)overtheamplitudes simulatedbyCoREAS(theleftfigureisslightlymodifiedfromRef.[17]).Forbothexperimentsthestandardreconstructionpipelinesareused,i.e.,Tunka-Rexamplitudes arethemaximumabsolutevaluesoftheelectric-fieldvectorinthebandof35–76MHz,andLOPESamplitudesarethemaximumofaHilbertenvelopetotheeast–west componentinthebandof43–74MHz.

Fig. 4. TheratioofreconstructedamplitudesofTunka-Rex(left)andLOPES(right)versuspredictionsfromair-showersimulationswithCoREASforprotonsandironnuclei asprimaryparticles.ForTunka-Rexthedepthoftheshowermaximumistunedinthesimulationstothemeasuredoneandtheamplitudeateachstationiscompared.For LOPESinsteadtheamplitudeat100m iscomparedforeachevent,whichisrelativelyindependentofthedepthoftheshowermaximum.ThemeanofaGaussiandistribution obtainedfromafitisusedtodefinetheenergyscaleusingCoREASasabenchmark.

applied a full detectorsimulation to the CoREAS output, i.e., the simulated amplitudes are directly comparable to the measured ones [36]. Unfortunately, KASCADE-Grande features no measure-mentofthedepthofshowermaximum,andthesimulationslikely have a different depth of shower maximum than the measured events,sincethisvariesfromshower toshower.Thisisimportant because the distance to the shower maximum affects the slope oftheradiolateraldistribution[37].Tominimizetheimpactonly the amplitude at 100m distance from the shower axis is used for the comparison, because at this distance the amplitude de-pendsleastonthedepthofshowermaximum,whichisoneofthe reasonswhythe same distancehasbeen selectedfor theenergy estimatorin the previous section. The mean ratiobetween mea-suredandsimulatedamplitudesat100m obtainedwithLOPESis F_LOPESp

=

0

.

92

±

0

.

02 for protonand FFe_LOPES

=

1

.

00

±

0

.

02 foriron primaries(seeFig. 3).

ForTunka-Rex we use thecomparison ofmeasurements from October 2012 to April 2013 with CoREAS simulations already showninRef.[17].Sincethesimulationstakeintoaccountthe sit-uation andresponse ofthe detectors,in contrastto the previous section the Tunka-Rex standard analysiscan be and isused. An-otherslightadvantageofTunka-Rex isthat Tunka-133provides a measurementofthe depthof shower maximum,whichhasbeen used to select simulations whose depth of shower maximum is consistentwithin 30g

/

cm2 _{to the measured one.Thus, the}

mea-sured and simulated amplitudes can be compared for each an-tenna individually irrespective of the distance from the shower axis. As for LOPES, the simulated events undergo a full detector simulation, includingantenna andhardware response, downsam-plinganddigitization,beforeaddingmeasurednoiseandapplying the same reconstruction algorithms as for the measured events. The mean ratiobetween theamplitudes measured by Tunka-Rex and simulated by CoREAS is Fp_TRex

=

0

.

88

±

0

.

01 for proton and F_TRexFe

=

0

.

97

±

0

.

02 forironprimaries(cf.Fig. 4).

Howisthisconnectedtotheenergyscale?Asystematicshiftin the energyscaleofthe hostexperiments,which isusedasinput for the simulations, also shifts the ratio between measured and simulatedamplitudeby:

F

=

Ereal Em

·

Freal (3)

withErealtherealenergyinnature,Emtheenergymeasuredwith

the energy scale of the host experiment, and Freal the ratio

be-tweentheamplitudepredictedbyCoREASandtherealamplitude innature.BecauseTunka-RexandLOPESarecomparedtothesame version of CoREAS, a possible constant scale mismatch between CoREASandnature, Freal,cancelsoutwhencomparingboth

exper-imentswitheachother.Thus,thederivedratioofenergyscales is

fsim

=

EKG ET133

=

FTRex FLOPES

.

(4)

184 Tunka-Rex and LOPES Collaborations / Physics Letters B 763 (2016) 179–185

Fig. 5. Energy spectra of cosmic rays from KASCADE-Grande [29] and Tunka-133[26]:normalizedfluxperenergy.Theenergyrangealsoobservedbytheradio extensionsTunka-RexandLOPESis1017_to1018_{eV.Withasystematicincreaseof}

KASCADE-Grandeenergiesby4% (oracorrespondingdecreaseofTunka-133 ener-gies)theaveragefluxperenergyofbothexperimentscanbebroughttoagreement inthisenergyrange.

The obtained ratios of scales are f_simp

=

0

.

96

±

0

.

05 and fFe sim

=

0

.

97

±

0

.

06 fortheprotonandironsimulations,respectively. This means that the KASCADE-Grande energyscale is lower than the Tunka-133energyscaleby

(

4

±

5

)

% or

(

3

±

6

)

%, respectively.The uncertainties include the statistical uncertainty of around 2% for each ratio and 5% from the analysis method and the different versions of the hadronic interaction model, which are added in quadrature.The uncertaintiesofthemethodarise becausethe ra-tio FTRex varies by several percent, depending on details of the

analysis procedure, such as bandwidth and model of the lateral distribution,which were not matchedbetween bothexperiments forthisanalysis.

5. Conclusion

We haveshownthat energyscales of differentair-shower ex-periments can be independently checked against each other by usingaccuratelycalibratedradiodetectors.Inparticularweapplied twodifferentmethodsforthiscross-checkontheradioextensions LOPESandTunka-Rex oftheKASCADE-GrandeandTunka-133 air-showerarrays:onemethodwhichreliespurelyonmeasureddata, butfeatures asystematic uncertaintycausedby thedifferent ob-servationlevels,andanothermethodbasedonsimulations taking intoaccountthedifferencesbetweentheexperimentalsettings.In additionto the method-dependentuncertainties between 5% and 7% bothmethods sharea correlatedsystematicuncertainty of7% due to the relative calibration of LOPES and Tunka-Rex. Finally, theinsufficientdescriptionofthezenithdependenceoftheLOPES antenna gain constitutes a dominating systematic uncertainty of about 10%. This shows the importance of accurate antenna cali-brationsforcurrentandfutureexperiments.Ascombinedresultof bothmethodsweshowthattheenergyscalesofKASCADE-Grande andTunka-133obtainedbysecondary-particleand air-Cherenkov-light detection, respectively, are consistent to an accuracy ofthe order of 10% – limited by systematic uncertainties of the LOPES experiment.

To cross-check this claim, published energy spectra of KASCADE-Grande [29] and Tunka-133 [26] are compared in the energyrange of1016.8 _{to 10}18.0_{eV (see Fig. 5). Assuming a}

sim-ple, constant energy shift between both experiments, and given thatbothexperimentsmeasurethesamecosmic-rayspectrum,the spectracanbebroughttomatchbyshiftingtheKASCADE-Grande energy upwards by 4% (or vice-versa down-shifting Tunka-133), i.e., fspec

=

0

.

96

±

0

.

06. The deviation is not statistically

signifi-cantandconfirmstheresultobtainedbytheradiomeasurements:

Fig. 6. Results from the comparisonof energy scalesbetween the experiments Tunka-Rexand LOPES,and theirhostsTunka-133 and KASCADE-Grande, respec-tively.Thevalues‘amplitude’,‘simulation’,and‘spectrum’ refertotheresults pre-sented inSecs.3,4,and 5,respectively, andtheindicateduncertaintiesare dis-cussedinSec.2andSec.3.

the energyscales ofKASCADE-Grande andTunka-133 are consis-tent anddiffer atmost by about 10%, despite the fact that they havebeen obtainedusingtwo differentmeasurementtechniques, namelyarraysofparticleandair-Cherenkovdetectors,respectively. Since both experiments rely on hadronic interaction models for theinterpretationoftheirdata,thisalsoindicatesthatthese inter-pretations areconsistent.The obtainedresultsare summarizedin Fig. 6.

Oneastrophysicalimplicationofthisresultisthatthe compar-isonoffeatures observedintheenergyspectrumis nowpossible withsmalleruncertainty,e.g.,whetherthekneeintheheavy com-ponent of the energy spectrum observed by KASCADE-Grande at about 1017_{eV [38], and a structure named as ‘second knee’}

ob-servedby severalexperimentsatabout3

·

1017eV[39,40]areone andthesameordifferentfeatures.

In the future, the accuracy of the presented methods can be furtherincreased,e.g.,bystudyingthesystematiceffectsregarding the shower inclination andthe observationlevels of the experi-ments inmore detailorby usingdifferentobservablesof the ra-dio signalsuchastheintegratedradiationenergy[19].Whilethis studyassumesaconstantvalue fortheenergyoffsetbetweenthe twoexperiments,givensufficientstatisticsandaccuracy,theoffset caninprinciplealsobestudiedasafunctionofenergy,orstudied separatelyfordifferentmassgroupsoftheprimarycosmicrays.

Moreover,themethodcanbeeasilyappliedtootherair-shower arraysfeaturing a radioextension, inparticular, AERA[41] atthe Pierre Auger Observatory [4],and LOFAR [18].When further im-provingthecalibrationaccuracyoftheantennaarrays,radio mea-surementscould alsobeused tocalibrate air-showerdetectorsor to combine and compare data from different experiments on a commonenergyscale.

Acknowledgments

The construction of Tunka-Rex was funded by the German Helmholtz Association and the Russian Foundation for Basic Re-search (grantHRJRG-303). Moreover, thiswork was supported by theHelmholtzAllianceforAstroparticlePhysics(HAP),byDeutsche Forschungsgemeinschaft (DFG) grant SCHR 1480/1-1, and by the RussiangrantRSF15-12-20022.LOPESandKASCADE-Grandehave beensupportedby theGermanFederalMinistryofEducationand Research. KASCADE-Grande is partlysupported by the MIURand INAFofItaly, thePolishMinistryofScienceandHigher Education and by the Romanian Authority for Scientific Research UEFISCDI (PNII-IDEI grant 271/2011). The authors acknowledge stimulating discussions within the ‘radio community’, inparticular with col-leaguesofthePierreAugerObservatoryandofLOFAR.

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