Radio Measurements of the Energy and the Depth of the Shower Maximum of Cosmic-Ray Air Showers by Tunka-Rex

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Radio measurements of the energy and the depth of the shower maximum of cosmic-ray air showers by Tunka-Rex

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Cosmic-Ray Energy Spectrum1017-1018.3 eV T. Abu-Zayyad, K. Belov, D. J. Bird et al. JCAP01(2016)052 c b hysics d P O. Krömer, a le b ic t A. Haungs, c and ar a f V.V. Prosin, a doi:10.1088/1475-7516/2016/01/052 strop D. Kostunin, R.R. Mirgazov, d A d M. Kleifges, O.A. Gress, a a L. Pankov, a R. Wischnewski b Y. Kazarina, E.E. Korosteleva, b N.M. Budnev, . Content from this work may be used a 3 osmology and and osmology a N. Lubsandorzhiev, d a C A. Pakhorukov, F.G. Schröder, a e T. Huege, b rnal of rnal Article funded byunder SCOAP the terms of the Creative Commons Attribution 3.0 License . ou An IOP and SISSA journal An IOP and Deutsches Elektronen-Synchrotron (DESY), Platanenallee 6, 15738 Zeuthen, Germany E-mail: [email protected] Institute of Applied Physics,Blvd Irkutsk Gagarina State 20, University Irkutsk, (ISU), Institute Russia for Nuclear PhysicsHermann-von-Helmholtz-Platz (IKP), 1, Karlsruhe 76344 Institute Eggenstein-Leopoldshafen, ofInstitute Germany Technology (KIT), for Data ProcessingKarlsruhe and Institute Electronics of (IPE), Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen,Skobeltsyn Germany Institute of NuclearLeninskie Physics, gory, Moscow GSP-1, State Moscow University 119991,Institute (MSU), Russia for Nuclear Research60th of October the Anniversary Russian st. Academy of 7a, Sciences, Moscow, Russia b c e d a f Any further distribution ofand this the work must title maintain of attribution the to work, the author(s) journal citation and DOI. The Tunka-Rex collaboration P.A. Bezyazeekov, Radio measurements of theand energy the depth ofmaximum the of shower cosmic-ray airTunka-Rex showers by J R. Hiller, G.I. Rubtsov, A. Zagorodnikov Received September 21, 2015 Revised December 22, 2015 Accepted January 7, 2016 Published January 27, 2016 E.N. Konstantinov, L.A. Kuzmichev, R. Monkhoev, JCAP01(2016)052 values consistent with the Tunka-133 max resolution of Tunka-Rex is approximately X max X 100 PeV applying a method using radio measurements performed & E 1509.05652 ultra high energy cosmic rays, cosmic ray experiments, cosmic rays detectors We reconstructed the energy and the position of the shower maximum of air . This resolution can probably be improved by deploying additional antennas and 2 , this is the first direct experimental correlation of radio measurements with a different, max Abstract. showers with energies with Tunka-Rex. An event-to-event comparisonair to showers air-Cherenkov with measurements the of Tunka-133works photomultiplier the reliably. array same The confirms Tunka-Rex that reconstructionon the methods radio CoREAS and reconstruction simulations absolute and scales have yield been energy tuned and 40 g/cm by further development ofyet the reveal any reconstruction principle methods, limitations. since the present analysisKeywords: does not ArXiv ePrint: measurements. The results ofuncertainties, two independent which measurement gives seasonsprecision agree additional of within Tunka-Rex confidence statistical is comparable in touncertainty on the the the Tunka-133 absolute precision radio scale of dominated 15X reconstruction. by %, the and amplitude exhibits calibration a The of the 20established % energy antennas. method. For At the moment, the JCAP01(2016)052 9 10 14 16 . max [2–5], too, but it X max max X X 2 a – 1 – eV. At higher energies the flux of cosmic-rays is too low 15 10 , and atmospheric depth of shower maximum . pr E E , but are limited to dark and clear nights. Detection of the radio emission max X Established air-shower techniques are the measurement of secondary particles on ground, 3.1 Asymmetry3.2 correction7 Lateral3.3 distribution function (LDF)8 Primary energy 5.1 Validity of5.2 the results Precision5.3 and accuracy Comparison with other experiments 14 11 12 the measurement ofimaging fluorescence detectors on or ground.energy The air-Cherenkov and latter for light two methods by haveby air a dedicated showers relatively is high telescopes an accuracy additionalthe technique, or for exposure. which the does non- The not radio suffer signal from this is intrinsic sensitive limitation to of the shower energy [1] and has not yet been demonstrateditive experimentally that with the those accuracy of for the both other variables is techniques, compet- as indicated by simulation-based studies, e.g., [6–8]. 1 Introduction After more than 100 yearsspectrum of of cosmic-ray measurements, the the primary mass particlesby composition is direct and relatively measurements, the well-known energy only in the energy range accessible to perform direct measurementsis with poorer statistical and significance.These relies indirect on Consequently, cosmic-ray the the measurements use knowledge the measurement the primary of atmosphere particle as secondary-particle can a cascadesthe be calorimeter. primary estimated called particle The from can, air energy the for showers. of Heavy energy example, primary be contained particles deduced in such as from the ironlight the shower. nuclei longitudinal particles on The shower average development. such type interact of as earlierfrom in protons. measurements the of atmosphere than the Thus, atmospheric the depth mass of composition the can shower maximum, be statistically estimated Contents 1 Introduction1 2 Experimental setup and data32 selection Reconstruction of energy and shower6 maximum 4 Results 5 Discussion 6 Outlook 7 Conclusion A Parametrization of LDF parameter B Comparison of both seasons 11 16 15 JCAP01(2016)052 max X at energies above the angle between ◦ α 50 ≤ θ , with α the spacing is approximately 2 [19]. For comparison, the average 2 is reconstructed from the steepness of the max – 2 – X is reconstructed from the flux of the Cherenkov light pr . E max X resolution of about 28 g/cm reconstruction have already been presented in reference [25] using max max X X . Since Tunka-133 triggers Tunka-Rex, the same air showers are measured 2 eV. Tunka-133 is fully efficient for all zenith angles 18 –10 eV [18], which covers the full energy range of Tunka-Rex. For Tunka-133 measurements, These combined measurements are used for a cross-check of both methods. In par- The parameters in the reconstruction methods have been determined from the simula- The main origin of the radio emission is the geomagnetic deflection of relativistic elec- Tunka-Rex [17] is the radio extension of the Tunka observatory for cosmic-ray air 16 2 . 16 the first season of Tunka-Rexhours measurements from of October measurements). 2012 The toseason same April of 2013 reconstruction (effectively method data 280 isand from now the applied October combined also 2013 to resultssented to the in and second April this the article. 2014 cross-checkTunka-Rex and between (effectively In Tunka-133 both reconstructions, 260 the which experimental measurement hours isof data seasons of used Tunka-Rex we for are to measurements), observe energy estimate pre- a and precision direct and accuracy correlation between the 2 Experimental setup and dataTunka-Rex started selection in autumn 2012antenna with stations 19 went antenna into stations,the operation and present in giving analysis. summer a 2013, In total 6 the number further central of area 25 covering antenna about stations 1 used km for ticular the precision of Tunka-Rex is estimated by a comparison of the energy and tions (cf. reference [8] forresults details), on and energy not and tuned against the Tunka-133 measurements. First amplitude-distance function. Using theseof methods, about Tunka-133 15 features %, an anddifference energy an between resolution the extremeorder cases of of 100 a g/cm puresimultaneously proton with and the a air-Cherenkov pure and iron the composition radio is detector. in the reconstructions to Tunka-133. Reconstructionwith methods CoREAS for simulations Tunka-Rex [20] haveprevious been (the theoretical developed radio predictions extension [6,7, ticular of22, LOPES CORSIKA23], [3], [21]) and AERA taking [11] experience into and by account LOFAR other [24]. experiments, in par- 200 m. The outer antennasarray contribute Tunka-133 only covers to the aphotomultipliers few in inner events the (see area outer figure1). withthe area. The radio 133 Upon air-Cherenkov and a photomultipliers, the coincidence and trigger air-Cherenkov features of detector the additional are photomultipliers, read both out in parallel. The electric field of the at 200 m distance to the shower axis, and trons and positrons inof the this shower, emission which induces is a proportional time-variable to current the [9]. shower energy The and amplitude to sin showers. Itstecting main the detector, Cherenkov Tunka-133, lightof is emitted 10 by an air-showers array in of the non-imaging atmospherethe in photomultipliers energy the de- of energy the primary range particle the geomagnetic field andtributes, the i.e., shower radio direction. emissionfront due On [10–12]. to a the The weaker time interference levelfootprint variation of the of [5, both Askaryan the13]. effects effect net leads con- emission charge Finally, to mechanisms excess the an [14–16]. in azimuthal refractive the asymmetry index shower of of the air radio causes Cherenkov-like effects for both 10 JCAP01(2016)052 the root-mean is the maximum N S have been selected ◦ 50 ≤ θ [17]. ◦ , atmospheric depth of the shower pr E reconstruction. 0 500 1000 max X East (m) – 3 – . Therefore, only events with ◦ 50 ≤ antennas 2012 antennas 2013 antennas photomultipliers θ events of of events season first season second −1000 −500 0 500 10 in at least three antenna stations, where the signal 1000

− 500

−1000 ot (m) North , and axis, i.e., the direction and point of incidence on the ground (= shower ≥ 2 ) max X . Map of the antenna array Tunka-Rex and its host experiment, the photomultiplier array S/N ( ≡ The reconstruction of Tunka-133 is fully efficient and has a reliable reconstruction for For the selection of Tunka-Rex events we applied a quality cut based on the signal-to- events with zenith angles noise ratio in individualSNR antenna stations. The signal has to exceed a signal-to-noise ratio, radio signal measured by Tunka-Rex isDetails reconstructed on in an the effective detector bandwidth of setup 35–76 and MHz. its calibration can be read infor reference the [17]. presentthe analysis shower (see provides:2). figure energy of For the these primary events particle the Tunka-133 reconstruction of of an envelopesquare on of the the electric-fieldpure electric strength background field of has a in the chanceefficiency a pulse, of and about time and purity. 5 % window the Given to before noise pass 25 the in antenna an signal. stations, individual antenna, this which This leads balances cut to is a set non-negligible probability such that core). For all Tunka-Rexthe events denser we spacing used of thewas the shower only photomultipliers core compared of used to Tunka-133background as as that pulses input, of cross-check: and the because excludedradio antennas. of events from and The the are air-Cherenkov direction arrival analysis, considered times if deviate false-positive, the by directions i.e., more reconstructed than contaminated from 5 by the Figure 1 Tunka-133. 18 antennas hadadditional been antennas available since have the goneshower start in cores of of operation the the onlycut first Tunka-Rex for on season events the in are the central October indicated second area 2012, for season with and both starting 500 7 m seasons. October radius The 2013. used dashed for The circle denotes the maximum JCAP01(2016)052 is max X . E geo B events of of events season first season second 200 m to the shower axis, since . 40° 2 > – 4 – axis 20° r geo 50 g/cm B θ S N ≤ ) radio max 2 MHz width (corresponding to 3 bins) at each integer 5 MHz . X 0 ( σ ± reconstruction we apply additional quality cuts: at least one antenna max agreement between the direction reconstructed by Tunka-Rex and Tunka- X ◦ W . Sky map of the Tunka-Rex events of both seasons. The efficiency rises with zenith angle Reconstruction of the electric-field strengths (= amplitude) in individual antenna sta- For the suppression of narrow-band radio-frequency interferences (RFI) we apply rect- tions is performed withPierre a Auger Collaboration modified [26]. versionto This of software the the applies all recorded ‘Auger known Offline’ signals,the experimental characteristics software various in developed components particular in by theFor the the the frequency-dependent signal reconstruction gain chain of as andantenna determined the pulse gain by electric-field distortion calibration is vector of measurements used, themeasurements. [17]. simulated which direction has dependence been of validated the for a fewangular selected band-stop directions filters of by calibration 133. Thus, the remainingFinally, data for set the isabove assumed to threshold be has practically to free be of false-positive at signals. a distance Figure 2 and is smaller for arrival directions close to the geomagnetic field that in a truemost of event these antenna false-positive stations signals,After we with two sort false-positive antenna the signals antennas stationsfrom by are failing their the contained. distance the to analysis SNR the Toby for cut, shower exclude a axis. the any station further particular withpositive antenna event. false-positive signals stations signal significantly are Thus, is impact excluded requiring the reduced the the to risk event 5 approximately that reconstruction, 10 %. they an are event If removed is surviving by false- contaminated the cut reconstructed from the slope ofMoreover, the the lateral shower distribution, core whichfigure1), requires and has a the to sufficient estimator lever be fornot arm. the exceed inside statistical a the reconstruction certain central uncertainty value: of area Tunka-Rex must of the array (dashed circle in JCAP01(2016)052 1 re- (2.1) max X reconstruc- , because the eV, all events ◦ max 17 50 and the amplitude X 10 ≤ · θ true E 140 iron proton . Most of the events used for 120 , max compared to the true pulse height parametrization X k 100 SNR meas eV. The fraction does not reach 100 % E − 17 1 80 r 1 adapted for Tunka-Rex. This normalization · . – 5 – signal-to-noise ratio (SNR) = 4 60 meas k E = 40 true E over the signal-to-noise ratio. 20 meas E 1

0.9 0.8 1.1

meas true

/ ε ε . Average ratio of the true pulse amplitude of CoREAS simulations An overview of the available event statistics is provided in table1, and figure4 shows , as already seen at the LOPES experiment27] [ and assumed for early experiments [ 28]. In earlier analyses we used a gliding median filter to suppress narrow-band RFI, but it turned out that this 1 true construction, the threshold is slightlyused higher: for energy above an reconstructiontion energy pass (see of also figure5). about the Apart 6 high-quality fromfraction cuts technical shown issues in required (e.g., figure5 for missingis or the malfunctioning efficiency antennas), of the Tunka-Rex for zenith angles filter significantly increases thecreasing impact the signal-to-noise of ratio. backgroundon Nevertheless, on the the the exact high-quality measured method events of amplitudes, used RFI in without suppression the significantly has present in- only analysis. minor influence because some Tunka-133 events havetechnical small issues in geomagnetic single angles. antenna Also, stations. there For were the occasional high-quality events used for the the distribution of the selected events over energy and with the signal-to-noise ratio SNR defined above. the energy reconstruction are at energies above 10 Figure 3 after adding measured noise (35, 40, . . . , 75 MHz), since these frequencies are often contaminated by RFI background. factor reflects the differentmaxima ways in how the the instantaneousfield, noise amplitude) which level corresponds and is to Tunka-Rex measuredcorrect the (root for in mean mean the power LOPES square average of (mean effect of noise). of of the Thus, local noise: electric we use the following formula to Since the radioby emission the from filter the thanstill air the on shower average narrow-band is increases disturbances. theE broadband, measured The it pulse background is height remainingWe significantly after studied less filtering this affected effect(figure3), by and found adding that measured theified background parametrization introducing to given a in about normalization reference factor 300 [27] CoREAS has to simulations be slightly mod- JCAP01(2016)052 (g/cm²) , of the max 900 max X . Tunka-133 Tunka-Rex N 800 √ in both seasons after ◦ 700 50 ≤ θ 600 500 reconstructed atmospheric depth of shower maximum X 25 22 9123 87 19

0 5

15 10 number of events N events of number – 6 – (280 effective hours) (260 effective hours) reconstruction three additional quality cuts are applied 18.4 max 18.2 X , and atmospheric depth of the shower maximum, ◦ 200 m 64 56 / eV) 5 pr 18 pr > Tunka-133 E Tunka-Rex ≤ 17.8 axis r 17.6 2 17.4 500 m) 17.2 50 g/cm r < 17 ≤ have been selected, since Tunka-133 is fully efficient for this zenith angle range. reconstructed primary energy lg (E ) ◦ 50 16.8 . Distributions of energy, . Statistics of Tunka-Rex events triggered at zenith angles radio max ≤ 3 stations with signal(Tunka-Rex, Tunka-133) 244 445 X 16.6 θ ( σ inner area ( after cut on≥ rejecting outlier stations] at least one antenna at Oct. 2012–Apr. 2013 Oct. 122 2013–Apr. 2014 147 Number of events first season of second season of

20 10 60 50 40 30 number of events N events of number Tunka-Rex events used inTunka-Rex the and Tunka-133. present Bars analysis. represent the The statistical figure uncertainty shows calculated as the reconstructed values by both Table 1 leaving 23 + 19 events for the two measurement seasons, respectively. Figure 4 3 Reconstruction of energyIn and the shower present maximum analysis,lateral the distribution, i.e., reconstruction the of dependenceaxis. energy of and the radio shower This amplitude maximumamplitude on approach is the at has based distance a to on been certainthe the the shower geomagnetic distance used angle is earlier. [1, correlateddistribution29–31]. depends with Moreover, Different on the it the experiments has primary distance been have energy, to shown after the shown that shower correcting the that maximum for shape [2,3,5]. the of the lateral certain quality cuts. Thethe cuts are number applied of consecutively surviving inused events the to after given reject application order. false-positive of The eventsare all contaminated event used numbers by cuts for denote background up energy pulses. to reconstruction. The that For remaining point. 91 + The 87 first events three cuts are reference is the fully efficienting Tunka-133 trigger. the quality The cuts total is larger numbertion [17], of is since more Tunka-Rex events in efficient pass- for contrast to inclinedwith air the showers. air-Cherenkov detection, Nevertheless, radio for detec- the present analysis only events JCAP01(2016)052 . , 1 1 g 2 α a a φ a max X and and 1 a 120 E 18 , and the fit result for pr E 17.8 . 17.6 , but also on the azimuth angle max r X / eV) pr 17.4 : reconstruction 17.2 – 7 – Energy lg (E max 17 is fixed using a parametrization depending on energy and 2 for energy reconstruction for X subset used a 16.8 to reconstruct the primary energy 120 Events passing Tunka-Rex quality cuts Events passing E 500 m). 16.6 0 1 r < 0.1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 and distance to the shower axis

, which is the amplitude at 120 m, and two shape parameters Fraction of triggered Tunka-Rex events Tunka-Rex triggered of Fraction α 120 E . Fraction of events which passes the quality cuts applied for the Tunka-Rex energy and ference of the geomagnetic and the Askaryan effects, and for the geomagnetic angle which describe the slopeare and fit the width to of thezenith the data Gaussian angle. points, LDF, respectively. parameter, at 180 m axis distance,the representing atmospheric the depth slope of of the the shower lateral maximum distribution, to reconstruct Our approach makes use of the fact that the asymmetry to first order only depends 1. We correct the lateral distribution for the azimuthal asymmetry caused by the inter- 3. We use the fit result 2. We fit a Gaussian LDF, the shape of which depends on three parameters: one scale reconstructions, respectively, in comparisonarray with in all the events inner triggered area by ( the fully efficient Tunka-133 Our reconstruction method in brief is: on the shower geometry, whichtime can measurements. be reconstructed independentlyazimuthal Based from asymmetry on the of LDF CoREAS by the simulations arrival footprint made is for parametrized the as function Tunka-Rex setup, of the the antenna position of each antenna relativea to two-dimensional the lateral shower distribution axis.To function maintain Fitting (LDF) events the with introduces asymmetry low additionaldescribed for station parameters in individual multiplicity, we reference [5]. events have [8], by developed which an is alternative well-suited approach for sparse arrays like Tunka-Rex. Figure 5 3.1 Asymmetry correction Because of the differentthe polarizations geomagnetic of effects [11, thegeomagnetic12 , radio32], angle emission the generated radio by amplitude the on Askaryan ground and depends not only on the JCAP01(2016)052 2 is the = 0, (3.2) (3.1) r max g X φ instead of asym ε , which is the 0 r E α , 2 the geomagnetic angle, of equation (2.1)), , α + sin 2 ) true α 0 E r shows little variation in the distance sin − g r φ ( asym 2 ε a cos . Thus, we use the following equation ) the amplitude after correction for the r α ) + ( 0 asym r ε cor E − r + 2 ( – 8 – 1 a , and the fitted scale parameter 5 % for the relative strength of the Askaryan effect. ), which is later used to fit a radially symmetric . r r depends on zenith angle and distance to the shower axis [12], 2 asym ( reconstruction. ε = 8 cor exp q E max 0 asym / r ε ) X E before and after correction, respectively, and the Tunka-133 g asym the azimuth angle relative to the shower axis (with 2 ε g r, φ ) = ( φ r E ( ) after correction for the azimuthal asymmetry and for the geomag- cor 15g/cm reconstruction is slightly improved for this event (Tunka-Rex r E ) = ). Especially for events with few stations, the asymmetry correction ( r ± 2 ( cor max E cor X E , and the lateral distribution can be fitted with a one-dimensional function r and 621 28 g/cm 2 ± ) the measured amplitude after noise correction ( g 085 the size of the asymmetry, and . r, φ ( is 657 = 0 15 g/cm E Figure6 shows an example event with many stations, where the asymmetry correction ± Although the size of the asymmetry 2 max asym using a constant valuemeasurements does mostly not fall describerange the in of lateral a 100–200 distribution m limited better. used zenith for Probably range. energy this and is Moreover, because Tunka-Rex simulation studies for Tunka-Rex have shown that parameterizing these dependences of using a constant typical value of with the amplitude netic angle as function of axis distance Using this parametrization, wethe correct azimuthal all asymmetry, measuredamplitude and amplitudes depends obtain in only a on individualthe one-dimensional the relative antennas lateral strength distance for of distribution to thegeometry, the in geomagnetic too, Lorentz shower which force, axis. namely the sinceto on this Simultaneously, we depends obtain the only correct the geomagnetic on for lateral-distribution corrected the angle function: shower amplitude with distance to the showerwhen axis, a station is inε the direction of the geomagnetic Lorentz force), asymmetry and theat geomagnetic each angle. antennaaround station, After the the this shower axis. lateral correctionthe Thus, shower distribution of to axis is the first order amplitude approximately the azimuthally measured amplitude symmetric depends only on the distance to the parameters of which depend on energy andleaves distance the energy to reconstruction the almost unchanged, showerout. since maximum. However, the the LDF fit averages the asymmetry X is important, and can have an effect3.2 on the energy reconstruction Lateral in distribution theThe function amplitude order (= (LDF) of electric field 10 strength) %. tional of to this one-dimensional the lateral shower distribution energy, isthe propor- because shape the of radio the emission lateraland distribution in has depends the two mainly shower main is onthe features: the coherent. existence, distance Moreover, first, size to the a andsecond, shower bump an position maximum exponential caused of tail by whichmaximum, [1, Cherenkov-like too. depend34], effects the on This [14, slope the meansfree15, of that distance parameters:32, which even to depends33], one a on thebump, for one-dimensional the shower and LDF the distance maximum; the should to energy slope contain thedistribution scale, of at shower function: the and least exponential two three fall-off. for For the this shape, purpose we namely use the the width following lateral of the 613 JCAP01(2016)052 the max max 0 X X r and the max to 120 m , i.e., the θ X 1 0 a r estimator: max LDF fit Energy estimator: 120 m amplitude at X slope at 180 m , and the remaining free , i.e, for different 0 pr r E , and to 180 m for the , the LDF is fit to the data 100 200 300 2 120 a E determines the slope of the expo- can simplify the reconstruction of 1 0 a . The shape parameter r pr , and weakly depends on energy and 1 0 E a affects the uncertainties and correlations 800 600 400 200

based on 1200 1000 r corrected amplitude (µV/m) amplitude corrected pr E sensitivity of the LDF. Furthermore, reducing is related to the width of the Cherenkov bump. – 9 – 2 a max X x (km) distance to shower axis (m) is correlated with . The shape parameter 0 2 r a using a parametrization depending on zenith angle as a free parameter would complicate the reconstruction of , and atmospheric depth of shower maximum is a purely technical parameter. Using a minimizing chi-square 2 2 , as these turned out to be the optimum values in the CoREAS pr a a 1 0 . However, the choice of E r a 2 a are determined using the equations presented in reference [8]. While (details in appendixA). After ﬁxing carries the whole 1 and max pr a 1 X E a , 0 r carries the whole sensitivity to the primary energy and E , and their statistical uncertainties. We set this distance parameter we use exactly the same equation as in the reference, i.e., the same values for all pr -1 0.5 - 0 0.5 1 0 50 150 250 350 120 . Example event. Left: footprint. Large crosses are triggered stations, and blue crosses are E E max max In the CoREAS simulations made for Tunka-Rex we observe that the scale parameter X 0 1 is strongly correlated with the primary energy -1 0.5 X

- 0.5 y (km) y pr 120 shape parameter for points. the number of free parametersthat in we the can LDF use fromTunka-Rex three events events to in with two the only brings present three the analysis). antenna additional advantage stations above3.3 threshold (about half Primary of energy the Energy zenith angle. Thus, fitting significantly. For this reasonand we to decided fix to the perform parameter the fit with only two free parameters, slope at 180 m axisThe distance is second strongly shape correlated with parameter the distance to the shower maximum. primary energy for the reconstruction of the primary energy E resulting function is exactly theparameters same, but just describedof with the a fit different set parameters,E of which values is for why the a specific choice of reconstruction based on simulation study. Figure 6 those stations with signalwithout above measurement the for signal-to-noise threshold.and this direction. event. The small The Right: dark-graycorrection, cross star but lateral is and with distribution a thecorrected station correction before line points. for (open indicate The the circles) light the geomagnetic and gray reconstructed point angle after shower is in (filled core a both circles)amplitude station cases. asymmetry at with the signal axis below The distance the LDF signal-to-noise is threshold. fitted to the nential fall-off, and theThe shape distance parameter parameter fit, the shape of the function does not depend on the choice of JCAP01(2016)052 (3.3) (3.4) Tunka-133 Tunka-133 E E

- +

Oct. 2012 - Oct. 2012 - Apr. 2014 Tunka-Rex Tunka-Rex E E

, is set to 120 m for 0 r , )) given in units of meters, and b ¯ , which has been determined L 1 + κ a 0.03 ± 0.02 0.17 ± 0.02 1

a 2 = σ Fitted Gauss: µ= Relative energy deviation: 2 log( -1 -0.75 -0.5 -0.250 0.25 0.50.75 1 0 B 60 50 40 30 20 10

+ Number of events of Number , and to 180 m for the determination of the 566 g/cm 93 of reference [8] is set to 1 instead and, . A − ( 120 E = − = 0 θ – 10 – b B , , 2 cos 120 / 1 ·E we use a simplification. The simplification is to assume with Tunka-Rex: det L pr X κ max E = = X 1864 g/cm pr reconstructions based on simulations were already presented in − max E and = is the atmospheric depth of the detector (typical value for the site X (radio): energy (EeV) max 2 pr 1:1 correlation (x = y) A X E Correlation with uncert. 93 or 1. Consequently, at the moment we lack experimental justification . . m), as an additional parameter and decided for the simpler solution. The 1 / a b Tunka-Rex (V 0.1 / = 955 g/cm is set to 0 . Correlation and relative deviation (= difference divided by average) of the shower energy b det Oct. 2012 - Apr. 2014 Oct. 2012 - X 005. As explained above, the technical parameter of the LDF, 6= 1. Moreover, there is no significant difference in the resulting energy precision . The energy and 1

0.1 = 884 EeV (air-Cherenkov): energy (EeV) energy (air-Cherenkov): Tunka-133 = 0 L reconstructed with Tunka-Rex radio and Tunka-133 air-Cherenkov measurements. parameters in the equation, for Figure 7 that the energyemission. is exactly This proportional means to that the the amplitude, exponent as expected for 100 % coherent thus, is not presentthat in with the the equation present used statisticsfor here. and quality The of reason thewhether for measured applying data, this we simplification have found is no evidence slope parameter reference [8]. The followingments section and presents the the comparison experimental to result the of Tunka-133 air-Cherenkov Tunka-Rex measure- measurements. 4 Results There is a clear correlationsured between by the Tunka-Rex energy and reconstructed from the the energy radio amplitude reconstructed mea- from the air-Cherenkov light measured for introducing simplification requires a different proportionality coefficient with the same setthe of reconstruction CoREAS of simulations. Summarizing, we use the following equations for where the determination of the amplitude at 120 m, used in theκ simulations), and theb parameters are determined with CoREAS simulations: ¯ JCAP01(2016)052 differ- Oct. 2012 - Oct. 2012 - Apr. 2014 max X [19]. This corresponds 2 (g/cm²): Tunka-Rex - Tunka-133 max reconstruction precision of 2 7 ±

- max 47 ± 5

X = σ Fitted Gauss: µ = (atmospheric depth between the shower scales of both detectors agree on an works reliably for the selected, high- -150 -100 -500 50 100 150 Difference in X 2 0 8 6 4 16 14 12 10 max

, when assuming that the resolutions of X Number of events of Number max max 2 2) %, which is only slightly larger than the X X ± , which reﬂects the combination of the unknown 2 – 11 – reconstructions the observed correlation is statistically 5) g/cm ± max X 1:1 correlation (x = y) Correlation with uncert. : distance to shower maximum (g/cm²) 200 400 600 800 1000 . Correlation and diﬀerence of the distance to Oct. 2012 - Apr. 2014 Oct. 2012 - Tunka-Rex For both the energy and Also for the position of the shower maximum there is a clear correlation between the

800 600 400 200

1000

: distance to shower maximum (g/cm²) maximum shower to distance : Tunka-133 compatible with a 1:1fitted correlation in of figures7 Tunka-133 andand8 are Tunka-Rex:scale compatible the offset). with means 0, of where This the 0 Gaussians means corresponds that to no the bias energy (= systematic and maximum and the shower core)measurements. as reconstructed with Tunka-Rex radio and Tunka-133 air-Cherenkov by Tunka-133 (figure7). Thisthe indicates presented that method. theTunka-Rex and energy When Tunka-133 reconstruction energy combining works values both is reliably seasons, (17 with the average deviation between the quality radio events.Tunka-Rex cannot Because be of estimated the veryence lower accurately. between both statistics, The detectors standard the is deviationTunka-Rex (47 uncertainty of and the theto Tunka-133 uncertainty a of radio-only 28Tunka-133 precision g/cm and Tunka-Rex of add better in squares than to 40 the g/cm total deviation. absolute level withinRex the scale measurement is uncertainty.With defined This already by consistent is CoREAS scales remarkable,calibration simulations there of since and is both the has no detectors Tunka- against need not each for been other. a tuned true against cross-calibration,5 Tunka-133. i.e., an explicit Discussion 5.1 Validity of theThe present results analysis issurements the of first the event-by-event comparison same of air showers. radio and Since air-Cherenkov both mea- detection methods are sensitive to the energy Figure 8 radio and air-Cherenkov reconstructions (figure8).statistics Due is to lower the than stricteragain quality for indicates cuts the the that energy event also correlation. the Still, reconstruction the of correlation is significant. This 15 % energy resolution reported by Tunka-133 [19]. JCAP01(2016)052 = max 2 X 28 g/cm · 2 precision is in- √ max X ), but observe a stan- 2 2 larger than the Tunka-133 √ . The derived Tunka-Rex precision is slightly 2 – 12 – 5) g/cm ± 2) %. Consequently, the energy precision of Tunka-Rex seems to ± 15 % = 21 % for the energy, which is slightly larger than the observed · 2 , as expected from CoREAS simulations when including realistic back- √ 2 , we would expect a standard deviation of the difference of max reconstruction of Tunka-133 for the second season. These values were revealed if Tunka-Rex had the same precision as Tunka-133 (28 g/cm X 2 max For Potential biases not excluded by the cross-check concern possible special events. For Consequently, the cross-check of both seasons cannot totally exclude all imaginable As additional cross-check of the validity of the results, we decided to blind the energy X standard deviation of (17 be at least equal to that of Tunka-133. 40 g/cm dard deviation of the difference of (47 better than 40 g/cm ground [8]. Since theantenna average spacing spacing, of this the Tunka-133 result photomultipliers is does half not of necessarily the average imply that the radio precision alone, i.e.: example, events with their showerlateral maximum very distribution close and tobe the a detector rejected small will by have footprint. areconstruction the very quality steep in Thus, cuts. the theyof full will Still, certain zenith events since likely is andFurthermore, Tunka-133 not at is not energy be high assumed fully range detected energies to efficientthis less or used cause and due than any will to in has a significant technical a third thisleading reasons bias of to reliable study, (missing in the small antenna the the events radio stations)rejection are observed non-detection amplitudes. or of rejected any correlations. due kind Thus, (cf. to of the figure5), specialthis small potential event and has can geomagnetic problem concern to angles of only be a a small studied bias fraction in of introduced more events. by detail Nevertheless, systematic the when biases larger implicit statistics in willdefinitely the be experimental confirms setup available. that or the in observed the correlations simulations are simulations, real. 5.2 but it Precision andThe accuracy spread of the deviationthe between same the events can Tunka-Rex and be used Tunka-133independent reconstruction to values Gaussian estimate for the uncertainties reconstruction precision ofdifference of both or Tunka-Rex. Assuming ratio reconstructions, between theor Tunka-Rex standard and relative deviation Tunka-133 uncertainties, is ofTunka-133, thus, the receptively. the this quadratic standard sum deviation If of should Tunka-Rex be the would a absolute factor feature of the same precision as to us onlycuts, after and we after we frozeappendixB decided thethe to reconstruction use results thestatistical method, of simplified uncertainties. both including equation seasons Thus, (3.4) digitalof we for are filters conclude energy implicit compared, reconstruction. and that tuning and our In on quality enough found results the to to are data cover be not the setantennas corrupted compatible slightly of in by within different the the any array first first kind configurations season year. in do both not Moreover, have seasons, the significant i.e., quality impact the cuts on missing any are of general the present results. and and the position of thetion maximum is of expected the between electromagneticsince radio shower component, the and a Tunka-Rex air-Cherenkov reconstruction strong observables. is correla- based133 This on is measurements simulations especially we and compared not noteworthy decided tuned with. against after Only the looking Tunka- details at ofband the interferences the or data reconstruction the method of exactand have the quality energy been first cuts. correlations season, Neither appear e.g., of or these the vanish. small filter decisions used made to the remove narrow- JCAP01(2016)052 ) for the radio max uncertainty of X ( σ ) the bias becomes max 2 X 900 g/cm & or determining the energy scale. For 2 reconstruction over energy or zenith L κ max X 350 g/cm . – 13 – as average of proton and iron simulations with the L κ of equation (3.4), the reconstructed energy would be 4 % L κ values approximately corresponds to the cut placed on the estimator In addition to the precision also the total accuracy is of importance.First, This is if dominated the fraction of the total primary energy going in the electromagnetic shower The Tunka-Rex energy scale defined by CoREAS simulations agrees within the un- Second, there is some freedom in the equation used for energy reconstruction. For Third, using CoREAS simulations we found a systematic bias of the energy reconstruc- Using CoREAS simulations we searched for systematic uncertainties potentially degrad- max by the 18 %systematic scale scale uncertainty uncertainties of have to the be amplitude considered: calibrationcomponent [17], was simulated but wrongly at inthe CORSIKA, least the same energy three scale value. further wouldstood, be However, wrong and by the as roughly electromagnetic estimatedis by shower only other component a experiments few is [35],simulates percent. relatively this the Moreover, uncertainty well we absolute on under- assume the radiocorrectly, that ‘invisible’ i.e., amplitude the energy with CoREAS emitted errors radio bywhich which extension the is are of CORSIKA electromagnetic supported small against showering by the component in recent calibration the experimental scale electromagneticThus, tests uncertainty shower the of [17, component parameters 18 depends].36 %, inthe on primary the Still, the particles, mass method the in of slightly fraction particular the depend also of primary the on energy particle. parameter the go- assumed mass composition of certainties to the Tunka-133Tunka-133 are scale. not This onlyother correlated, means confirmation, but that that in the CoREAS addition seems measurements agree to of on predict Tunka-Rex the an and radio absolute signal level, correctly. which is an- angle, but we didthe not radio find any technique significant mightevents effect. of become The even equal finally higherX to achievable quality the are one used.statistical of The uncertainty the spread of air-Cherenkov between Tunka-Rex.used technique, the This to Tunka-133 when means and set that stronger Tunka-Rex this quality cuts estimator when is higher reliable statistics and are can available. be the present analysis, we determined larger than 10 %, andsystematic will uncertainties have are to small be compared totion corrected the for of scale such 18 uncertainty %. rare of the events. Thus, amplitude the Consequently, calibra- all total known accuracy of the Tunka-Rex energy scale is approximately 20 %. example, if we had usedthen exactly the the reconstructed energy equation primaryhave of energy been reference would [8] tuned be instead against about ofthe the 10 equation % same 18 (3.4), % lower, set although scale of bothstudy CoREAS uncertainty equations of simulations. of the the This reconstruction difference amplitudebecomes method is calibration, available. well will but within become indicates necessary that once a a more moretion detailed accurate depending calibration on the distancedifference to between proton- the and shower maximum. iron-initiatedclose showers, or The and far mean distances thus effect to negligible. is the smaller However, shower maximum for than ( very the hadronic interaction modeliron QGSJET-II.04 composition [37]. to determine smaller If or we larger, had respectively. taken a pure proton or a pure ing the resolution further, in particular biases of the trinsically worse than theTunka-133 and air-Cherenkov Tunka-Rex precision. resolutions compare Instead, forthe later equal Tunka-Rex studies precision detector will will spacing, and improve show by due how how to the much additionally deployed antennas. JCAP01(2016)052 max X recon- sensitivity max X max X , when using a denser 2 reconstruction by Tunka-Rex is not yet measurements. Thus, with the present measurement. This also gives more con- reconstruction, there is room for improve- max max max X X X max X – 14 – resolution. Moreover, additional methods for resolution of Tunka-Rex. max max X X could be exploited when more antenna stations contribute to the fit. 2 a reconstructions based on absolutely-calibrated radio measurements have reconstruction based on a fitted LDF (like in our approach), the precision max X max reconstruction, the resolution of LOPES has been significantly worse, using a sim- reconstruction is also based on CoREAS simulations using two different methods. X at LOFAR is only slightly better than our resolution [5]. However, with a more max max Compared to this study the antenna density will be tripled. At each of the 19 Tunka clus- The most important scientific value of the present analysis is the experimental com- max X X X ment. As shown by LOFAR [4],radio the array precision can and be a asand good simulation-driven to as method. further 20 g/cm improveaverage Thus, the event we reconstruction will plan method. contain todistributions more With deploy with antenna an more additional stations increased free antennas with parameters.of antenna signal, the density, For LDF the which example, parameter the allows weak fitting energy of and lateral ters in the inner area,be already deployed in now summer a 2016. secondthe antenna This core station enables resolution is an affect deployed, experimental the and test a how the third antenna one density will and fidence in the resultswith the of same other CORSIKA radio + arrays CoREAS Monte whose Carlo reconstruction codes. procedures are6 developed Outlook The presently achieved accuracy forat energy and its principle limits. In particular for the of been compared to air-Cherenkovsignal measurements. on While the the longitudinal principlecomparing shower sensitivity development LOPES of was lateral already the distributionsdetector demonstrated radio to [2], experimentally measurements KASCADE by did ofcomparison not the of feature KASCADE Tunka-Rex and direct muon-tracking Tunka-133,is for the directly first cross-checked with time an the independent radio reconstruction of struction based on other quantitiesracy. of The the shape radio of signal the wavefront can [41] be can be used reconstructed to by improve arrival the time total measurements, and accu- computing-intensive method using manycision simulations by for LOFAR each isplanned individual at deployment event of least [4], additional twice antennas,methods the as also could pre- good further increase improvements as the in ours. the reconstruction This indicatesparision that of in radio addition measurementsenergy to against and the another, established technique. For the first time, With an pler method inLOFAR a is located more in radio-loudIts a environment more than radio-quiet environment Tunka-Rex. similar to The the much situation denser of array Tunka-Rex. 5.3 Comparison with otherThe experiments 15 % energylike precision AERA of [38], Tunka-Rexaround is LOPES at 20 [3], %. least andAERA as CODALEMA The [38] good [39], and Tunka-Rex as whichand scale LOPES that all particle of [36], uncertainty reported measurements other of which onthe energy radio compared 20 ground. % radio precisions arrays, the amplitude roughly LOFAR radiocuracy with as corresponds measurements are similar well to to limited accuracy features air-fluorescence that byFor [40], an the but absolute of poor experimental calibration of checks energy of resolution the of energy the ac- LORA particle detector array [5]. JCAP01(2016)052 this is [44]. In max X max X eV. The reconstruction 17 for Tunka-133 [19]) and by 2 10 & , and can be slightly increased by pr 2 E accuracy under practical conditions. max X – 15 – for the Pierre Auger Observatory [35]). Neverthe- 2 reconstructed from Tunka-Rex and Tunka-133 mea- max X precision of Tunka-Rex is roughly 40 g/cm max X Finally, the absolute energy measurement of air-showers with a radio array opens The statistics of Tunka-Rex will be dramatically increased by joint measurements with The Tunka-Rex energy precision seems to be at least as good as the published Tunka-133 The prospects to cross-calibratemeasurements. the energy This scales aspecttenna is of arrays worth different can to air-shower be be experiments a investigated via very more economic radio deeply, add-ons in to particular existing7 since detectors an- as shown Conclusion by Tunka-Rex. We have compared energy and the slope of the frequency spectrumby [42] how by much sampling these the methods pulse can shape. increase Future the studies total will show addition, the Tunka-Grande measurementon accuracy hybrid will measurements be with enhanced Tunka-Rex. by a cross-calibration setting stricter quality cuts at thedistinguish cost light of from statistics. heavy primary Thisachieved particles. resolution by is The non-imaging sufficient resolution air-Cherenkov to is statistically measurements worseair-fluorescence (28 than g/cm measurements the (20 one g/cm currently the newly deployedtrigger particle-detector array for Tunka-Grande Tunka-Rex. [43],where which Tunka-Grande each provides consists station asurement of features day-time of 19 scintillator secondary stations, detectorsfor air-shower one on the electrons present at ground and analysisstruction each and focused muons, of inner under the on respectively. cosmic-ray cluster, the ground, compositionare feasibility possible While for relevant. systematic of uncertainties unimportant mea- the like reconstruction UsingTunka-Grande selection such biases methods, the systematic for additional uncertainties recon- additional can statistics be muon and checked measurements independent experimentally. cansince measurements Moreover, enhance the the provided electron-muon the by ratio total provides accuracy complementary for mass the information mass to composition, surements of the same air showers in the energy range resolution of 15 %. Theof total the scale uncertainty amplitude of Tunka-Rexthe calibration, is dominated scale and by the uncertainty in uncertainty calibration of total uncertainty dominates particle is the total detector in scalein uncertainty the the arrays, of calibration Tunka-Rex, accuracy order like any will improvement of directly KASCADE-Grandefurther propagate efforts 20 to [45]. %. the on energy-scale the accuracy.as This calibration Since Consequently, will the is the be comparable currently necessaryObservatory, to leading to the increase fluorescence scale the and accuracy accuracyreasonable to air-Cherenkov of reach the for techniques. fluorescence same future level measurements radioavailable At around-the-clock. is measurements, which the Hence, 14 % unlike radio Pierre fluorescence measurements [35].energy can measurements Auger be scale are used This of to air-shower now determine the measurements. is absolute in methods have been developed andtension tuned CoREAS. using For both simulations withTunka-133 parameters consistently CORSIKA we in and find two its a seasons radioradio strong of ex- correlation measurements data between are taking. Tunka-Rex indeed This and the sensitive confirms first experimentally to direct that confirmation energy based the technique, and on namely shower a air-Cherenkov maximum. cross-check measurements. with For a different, established experimental JCAP01(2016)052 max had (A.2) (A.1) X defin- 2 max a X . , EeV pr · , the shape of the Gaussian EeV E pr 2 · pr E 2 m E 5 m − 5 − 10 · θ , 10 · 44 . 63 ) cos 2 . 1 pr a + 2 E 2 − ( 1 2 m 22 1 5 a m – 16 – − 5 − − 10 ) · 10 pr · E 45 ( . 3 19 21 . for the second season based on the radio measurements. − a can either be solved by an iterative approach, or by using a = = 0 max ) = pr 22 21 X pr E a a θ, E ( 2 . We decided for the latter solution, using the energy estimator based a pr parameter is a function of the primary energy E 2 a reconstructions9 (figures and 10) separately for both seasons. The results of both max The plots in this appendix show the comparison of the Tunka-Rex and Tunka-133 energy Since the For astrophysical applications the total accuracy for the reconstruction of the mass X and Only afterwards, Tunka-133 unblinded their reconstruction of the second season to us. on a simpler exponentialworse LDF than presented than in in reference our [17], more since advanced approach its here. precisionB is only slightly Comparison of bothThe seasons data set ofcheck Tunka-Rex of is the split validity in of our two seasons methods, of the Tunka-133 about reconstruction equal of size. energy and As additional cross- LDF used to reconstructreciprocal the dependence primary on energypre-estimate depends for implicitly on the energy itself. This been blinded for the secondvalues season. had Only been for known, theof first and the season were the Tunka-Rex used Tunka-133 energypredicted methods. for and the occasional energy After cross-checks during and we the frozen development the Tunka-Rex reconstruction methods, we In the Gaussian lateral distribution function (LDF, equation (3.2)), the parameter composition as a function ofto energy yet-unknown counts, extra-galactic e.g., toRex cosmic-ray better [46]. sources study the assumed transition Tunka-Rexcurrent in from will Tunka-133 Galactic the provide analyses energy additionalair-showers are range by statistics limited Tunka-Rex of exactly and by Tunka- surements in Tunka-Grande statistics. can started the be in used energy Moreover, autumn toradio range hybrid enhance 2015. and the where muon measurements total These measurements. of accuracy hybrid for mea- the mass composition byAcknowledgments combining Tunka-Rex has been fundeddation by for the Basic Germanthe Helmholtz Research Helmholtz association (grant Alliance and15-12-20022. HRJRG-303). for the Russian Astroparticle Foun- Moreover, Physics this (HAP), and work by wasA the supported Russian by grant Parametrization RSF of LDF parameter less, the resolution of Tunka-Reximprovements is of not the yet reconstruction at method, its and limit and by can deploying likely additional be antennas. increased by further ing the bumpsimulations has made for been the set situation of by Tunka-Rex the [8]: following parameterization determined with CoREAS JCAP01(2016)052 1 Tunka-133 Tunka-133 0.75 E E

- + 0.5 Tunka-Rex Tunka-Rex second season E E

0.25 0 (radio): energy (EeV) 1:1 correlation (x = y) Correlation with uncert. -0.25 values of the events. However, Tunka-Rex -0.5 0.11 resolution. 0.02 ± 0.02 0.18 ± 0.03

max = -0.75 X second season max σ Fitted Gauss: µ = Relative energy deviation: 2 X -1 1

5 0

0.1

30 25 20 15 10 (air-Cherenkov): energy (EeV) energy (air-Cherenkov): Tunka-133 Number of events of Number 1 – 17 – Tunka-133 Tunka-133 0.75 E E

- +

first season 0.5 Tunka-Rex Tunka-Rex E E

0.25 0 (radio): energy (EeV) 1:1 correlation (x = y) Correlation with uncert. -0.25 500 m, dashed circle in figure1) was discovered a posteriori by us, i.e., after -0.5 . Comparison of the first and second season: reconstructed energy (cf.7). figure Tunka-Rex 0.11 0.03 ± 0.03 0.19 ± 0.03

r <

= -0.75 σ Fitted Gauss: µ = first season Relative energy deviation: 2 -1 As supplementary material we will upload the list of the events used for the present The original event lists for the ﬁrst ‘tuning’ and second ‘prediction’ seasons, as Figure 9 5 0 15 10 30 25 20 1

0.1 Number of events of Number (air-Cherenkov): energy (EeV) energy (air-Cherenkov): Tunka-133 analysis. This list contains the reconstructed energy and seasons are consistent within statisticalinner uncertainties. area The ( quality cut on events inside of the we had frozen thefive reconstruction additional methods events are for presentare the (two outside unblinding in of procedure. the the first Thus, inner season, in area three and figure in slightly10 the degrade second the season), which the values should notmass composition. be used While unimportant for forTunka-133 reconstruction reconstruction, the present of for study such the comparingwhich the analyses cosmic-ray Tunka-Rex cannot to selection energy be the biases spectrum derived have from or to the the be event list taken alone. into account, JCAP01(2016)052 150 100 (2012) 071101 second season 50 D 85 0 1:1 correlation (x = y) (g/cm²): Tunka-Rex - Tunka-133 Correlation with uncert. -50 max Phys. Rev. : distance to shower maximum (g/cm²) , 2 ± 13 2

59 ± 9 59 -100

Pr. Elem. Part. Cosmic Ray Phys. = , Fitted Gauss: µ = - σ 200 400 600 800 1000 second season Tunka-Rex -150 Difference in X

2 1 0 9 8 7 6 5 4 3

800 600 400 200 events of Number

1000

: distance to shower maximum (g/cm²) maximum shower to distance : Tunka-133 – 18 – Experimental evidence for the sensitivity of the 150 H9AoxFywAt’ for the tuning season, and 100 first season ]. 50 SPIRE IN 0 ][ 1:1 correlation (x = y) Correlation with uncert. (g/cm²): Tunka-Rex - Tunka-133 -50 max Radio Emission From Extensive Air Showers : distance to shower maximum (g/cm²) collaboration, W.D. Apel et al., z3DumFNfsq’ for the prediction season. All these events are also con- 51 ± 7 15 ± 10 -100

. Comparison of the ﬁrst and second season: distance to shower maximum (cf. ﬁgure8). 200 400 600 800 1000 = first season σ Fitted Gauss: µ = (1971) 171. Tunka-Rex -150 Difference in X arXiv:1203.3971 LOPES 10 air-shower radio signal to the longitudinal shower development [ 0 6 5 4 3 2 1 9 8 7

800 600 400 200

1000

Number of events of Number : distance to shower maximum (g/cm²) maximum shower to distance : Tunka-133 [2] [1] H.R. Allan, Figure 10 created after freezinghttp://www.ikp.kit.edu/tunka-rex/ the reconstruction methods,They but can before be unblinding, decryptedopenssl are using the aes-256-cbc available following at: -d LinuxThe command: -in encryptedFile passwords -out decryptedFile are ‘TunkaRex1 ‘TunkaRex2 tained in the above-mentioned list submitted as supplementary material. References JCAP01(2016)052 ] 05 ]. ]. Royal Nucl. JCAP , SPIRE , IN SPIRE ]. IN ][ (2014) 062001 ][ arXiv:1107.0665 (2015) 89 SPIRE (2015) 04002. ]. IN ]. D 90 (1966) 206. 99 (2014) 082003 A 802 (2008) 96 SPIRE SPIRE 289 IN , in proceedings of the IN D 90 30 The Lateral Distribution Coherent Cherenkov Radiation 12th ICRC, Hobart, Tasmania, ][ ][ (2015) 50[ arXiv:1008.3308 (2011) 061101[ Phys. Rev. arXiv:1402.3677 (1973) 892. , 69 6 107 (2014) 014. Phys. Rev. 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A 662 The Pierre Auger Cosmic Ray Observatory Energy Estimation of Cosmic Rays with the On noise treatment in radio measurements of CORSIKA: A Monte Carlo Code to Simulate A Realistic Treatment of Geomagnetic Cherenkov Astropart. Phys. 75 Detecting cosmic rays with the LOFAR radio Astropart. Phys. (2005) 313[ Energy Estimation for Cosmic Rays Measured with – 20 – , Lateral Distribution of the Radio Signal in Extensive Improved absolute calibration of LOPES ]. , Frequency Spectrum of Air Shower Radio Pulses Detection and imaging of atmospheric radio flashes Measuring a Cherenkov ring in the radio emission from ]. 435 Astropart. Phys. AIP Conf. Proc. , , arXiv:1502.01323 SPIRE (2013) A98[ IN ]. SPIRE arXiv:1507.07389 ][ IN ]. Nature 560 ]. ][ , SPIRE IN Nucl. Instrum. Meth. Phys. Atom. Nucl. SPIRE (2015) 172[ ][ , SPIRE , , ,FZKA-6019 Forschungszentrum Karlsruhe GmbH, Karlsruhe Germany IN IN (2016) 72[ ][ ][ 75 QGSJET-II: Results for extensive air showers collaboration, A. 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