The energy spectrum of cosmic-ray electrons at TeV energies F.Aharonian1,13, A.G.Akhperjanian2, U.BarresdeAlmeida8,∗ A.R.Bazer-Bachi3,Y. Becherini12,B. Behera14, W. Benbow1, K.Bernlo¨hr1,5, C. Boisson6, A. Bochow1, V. Borrel3, I. Braun1, E. Brion7, J. Brucker16, P. Brun7, R. Bu¨hler1, T. Bulik24, I.Bu¨sching9,T.Boutelier17,S.Carrigan1,P.M.Chadwick8,A.Charbonnier19,R.C.G.Chaves1,A.Cheesebrough8,L.-M.Chounet10, A.C.Clapson1, G. Coignet11, L.Costamante1,29, M.Dalton5, B.Degrange10, C. Deil1, H.J. Dickinson8, A. Djannati-Ata¨ı12, W. Domainko1, L.O’C.Drury13, F. Dubois11, G. Dubus17, J. Dyks24, M. Dyrda28, K.Egberts1,† D. Emmanoulopoulos14, P.Espigat12, C.Farnier15,F. Feinstein15, A.Fiasson15, A.Fo¨rster1,G. Fontaine10, M.Fu¨ßling5,S. Gabici13,Y.A.Gallant15, L.G´erard12,B. Giebels10, J.F.Glicenstein7,B. Glu¨ck16,P. Goret7, C.Hadjichristidis8, D.Hauser14, M.Hauser14,S. Heinz16, G. Heinzelmann4,G. Henri17,G. Hermann1,J.A.Hinton25,‡ A.Hoffmann18,W.Hofmann1,M.Holleran9,S.Hoppe1,D.Horns4, A.Jacholkowska19,O.C.deJager9,I.Jung16,K.Katarzyn´ski27,S.Kaufmann14,E.Kendziorra18,M.Kerschhaggl5,D.Khangulyan1, B. Kh´elifi10, D.Keogh8, Nu. Komin15, K.Kosack1, G. Lamanna11, J.-P.Lenain6, T.Lohse5, V.Marandon12, J.M.Martin6, O.Martineau-Huynh19,A.Marcowith15,D.Maurin19,T.J.L.McComb8,C.Medina6,R.Moderski24,E.Moulin7,M.Naumann-Godo10, M.deNaurois19,D.Nedbal20,D.Nekrassov1,J.Niemiec28,S.J.Nolan8,S.Ohm1,J-F.Olive3,E.deOn˜aWilhelmi12,K.J.Orford8, 9 J.L.Osborne8,M.Ostrowski23,M.Panter1,G.Pedaletti14,G.Pelletier17,P.-O.Petrucci17,S.Pita12,G.Pu¨hlhofer14,M.Punch12, 0 A.Quirrenbach14,B.C.Raubenheimer9,M.Raue1,29,S.M.Rayner8,M.Renaud1,F.Rieger1,29,J.Ripken4,L.Rob20,S.Rosier-Lees11, 0 G.Rowell26,B.Rudak24,C.B.Rulten8,J.Ruppel21,V.Sahakian2,A.Santangelo18,R.Schlickeiser21,F.M.Scho¨ck16,R.Schro¨der21, 2 U.Schwanke5,S.Schwarzburg18,S.Schwemmer14,A.Shalchi21,J.L.Skilton25,H.Sol6,D.Spangler8,L . Stawarz23,R.Steenkamp22, C.Stegmann16,G.Superina10,P.H.Tam14,J.-P.Tavernet19,R.Terrier12,O.Tibolla14,C.vanEldik1,G.Vasileiadis15,C.Venter9, n a J.P.Vialle11, P.Vincent19, M.Vivier7, H.J.Vo¨lk1, F. Volpe10,29, S.J. Wagner14, M.Ward8, A.A.Zdziarski24, and A. Zech6 J 1 Max-Planck-Institut fu¨r Kernphysik, P.O. Box 103980, D 69029 Heidelberg, Germany 2 Yerevan Physics Institute, 2 Alikhanian Brothers St., 375036 Yerevan, Armenia 6 3 Centre d’Etude Spatiale des Rayonnements, CNRS/UPS, 9 av. du Colonel Roche, BP 4346, F-31029 Toulouse Cedex 4, France ] h 4 Universit¨at Hamburg, Institut fu¨r Experimentalphysik, p Luruper Chaussee 149, D 22761 Hamburg, Germany - 5 Institut fu¨r Physik, Humboldt-Universit¨at zu Berlin, Newtonstr. 15, D 12489 Berlin, Germany o 6 LUTH, Observatoire de Paris, CNRS, Universit´e Paris Diderot, 5 Place Jules Janssen, 92190 Meudon, France tr 7 IRFU/DSM/CEA, CE Saclay, F-91191 Gif-sur-Yvette, Cedex, France s 8 University of Durham, Department of Physics, South Road, Durham DH1 3LE, U.K. a [ 9 Unit for Space Physics, North-West University, Potchefstroom 2520, South Africa 10 Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France 2 11 Laboratoire d’Annecy-le-Vieux de Physique des Particules, CNRS/IN2P3, v 9 Chemin de Bellevue - BP 110 F-74941 Annecy-le-Vieux Cedex, France 4 12 Astroparticule et Cosmologie (APC), CNRS, Universite Paris 7 Denis Diderot, 9 10, rue Alice Domon et Leonie Duquet, F-75205 Paris Cedex 13, France § 8 13 Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2, Ireland 3 14 Landessternwarte, Universit¨at Heidelberg, K¨onigstuhl, D 69117 Heidelberg, Germany 1. 15 Laboratoire de Physique Th´eorique et Astroparticules, 1 CNRS/IN2P3, Universit´e Montpellier II, CC 70, 8 Place Eug`ene Bataillon, F-34095 Montpellier Cedex 5, France 0 16 Universit¨at Erlangen-Nu¨rnberg, Physikalisches Institut, : Erwin-Rommel-Str. 1, D 91058 Erlangen, Germany v 17 Laboratoire d’Astrophysique de Grenoble, INSU/CNRS, i X Universit´e Joseph Fourier, BP 53, F-38041 Grenoble Cedex 9, France r 18 Institut fu¨r Astronomie und Astrophysik, Universit¨at Tu¨bingen, Sand 1, D 72076 Tu¨bingen, Germany a 19 LPNHE, Universit´e Pierre et Marie Curie Paris 6, Universit´e Denis Diderot Paris 7, CNRS/IN2P3, 4 Place Jussieu, F-75252, Paris Cedex 5, France 20 Institute of Particle and Nuclear Physics, Charles University, V Holesovickach 2, 180 00 Prague 8, Czech Republic 21 Institut fu¨r Theoretische Physik, Lehrstuhl IV: Weltraum und Astrophysik, Ruhr-Universit¨at Bochum, D 44780 Bochum, Germany 22 University of Namibia, Private Bag 13301, Windhoek, Namibia 23 Obserwatorium Astronomiczne, Uniwersytet Jagiellon´ski, Krak´ow, Poland 24 Nicolaus Copernicus Astronomical Center, Warsaw, Poland 25 School of Physics & Astronomy, University of Leeds, Leeds LS2 9JT, UK 26 School of Chemistry & Physics, University of Adelaide, Adelaide 5005, Australia 27 Torun´ Centre for Astronomy, Nicolaus Copernicus University, Torun´, Poland 28 Instytut Fizyki Ja¸drowej PAN, ul. Radzikowskiego 152, 31-342 Krak´ow, Poland and 29 European Associated Laboratory for Gamma-Ray Astronomy, jointly supported by CNRS and MPG 2 The very large collection area of ground-based γ-ray telescopes gives them a substan- tial advantage over balloon/satellite based instruments in the detection of very-high-energy (>600 GeV) cosmic-ray electrons. Here we present the electron spectrum derived from data taken with the H.E.S.S. system of imaging atmospheric Cherenkov telescopes. In this measurement, the first of this type, we are able to extend the measurement of the elec- tron spectrum beyond the range accessible to direct measurements. We find evidence for a substantial steepening in the energy spectrum above 600 GeV compared to lower energies. PACSnumbers: 95.85.Ry In stark contrast to hadronic cosmic rays (CRs) like events in regions far from γ-ray sources and sub- the lifetime and hence propagation distance of CR tractionofthe remaininghadronicCRbackgroundusing electrons in the very-high-energy regime is severely air-showersimulations. The data used were acquired us- limited by energy losses via synchrotron radiation ing the complete 4-telescope array during 2004 to 2007. and inverse Compton scattering. The lifetime of a Alldatapassingqualityselectioncriteria,withzenithan- very-high-energy electron can be expressed as: t ≈ glessmallerthan28◦,andtargetingextragalacticsources, 5×105(E/1TeV)−1((B/5µG)2 +1.6(w/1eVcm−3))−1 wereusedinthisanalysis,amountingto239hoursoflive- ◦ years, where w is the energy density in low frequency time. Only the central 3.0 of the field-of-view was uti- photons (hν ≪ 0.1 eV) in the interstellar medium and lized, with regionswithin 0.4◦ of any knownor potential B is the mean interstellar magnetic field. In standard γ-ray source excluded. The energy is reconstructed us- diffusion-dominatedmodelsofGalacticcosmic-raytrans- ingstandardmethods. Theeffectivecollectionareausing port this implies that the sources of TeV electrons must the technique described below is energy dependent and be local (< 1 kpc distance) as discussed in e.g. [1] and reaches≈5×104m2at1TeV.Thetotaleffectiveexposure [2]. A second consequence of these energy-dependent of this data set at 1 TeV is therefore ≈8.5×107 m2srs. losses is that the electron spectrum is steeper than that The most critical aspect of electron analysis is the ef- of the hadronic CRs (∼E−3.3 cf. E−2.7). All measure- ficient rejection of the hadronic background. Given the ments so far have utilized balloon or satellite borne in- relatively high flux of cosmic electrons with respect to strumentation(see[3]forareview). However,therapidly typicalγ-raysourcesitisappropriatetomaketightselec- declining flux makes such direct measurements at high tion cuts to achieve the best possible signal/background energies difficult. It has been suggested ([4]) that the ratio. Very hard event selection, including the require- very large collection area of ground-based imaging at- ment that all four H.E.S.S. telescopes triggered in the mospheric Cherenkov telescope (IACT) arrays could be event, leads to a greatly increased energy threshold of usedtoextendCRelectronspectrummeasurementsinto ≈600GeV.ARandom Forest [9](seealso[10])approach the TeV domain. The challenge for such instruments (as wasusedtoconvertimageinformationfromthefourcam- indeed for allCR electronmeasurements)is to recognize eras into a single parameter ζ describing the degree to electrons against the much more numerous background which a shower is electron-like. The primary input pa- of hadronic CRs. The recent improvements in hadron- rameters to the Random Forest algorithm are the Hillas rejectionpowerachievedbytheHighEnergyStereoscopic moments[11]oftheimagesrecordedineachtelescope. A System (H.E.S.S.) instrument have now made such a ζ value of zero corresponds to a shower which is almost measurement possible. certainlybackground,andavalueofoneisassignedifthe shower is almost certainly an electron. Random Forests H.E.S.S. is an array of four imaging atmospheric weretrainedinfiveenergybandsusingsimulatedelectron Cherenkov telescopes situated in the Khomas Highland showersanddatatakenfromemptyregions. Tosubtract ofNamibia[5]. Thearrayissensitivetoγ-rays(andelec- the hadronic background the ζ distribution of protons trons)aboveathresholdof≈100GeV.Thesensitivityof 10 and nuclei must be known. For this purpose sets of 10 the array to extended γ-ray emission has been demon- proton showers and showers of heavier nuclei were simu- strated with the mapping of supernova remnant shells lated with CORSIKA [12] using both the SIBYLL [13] ([6], [7]), and the diffuse emission around the Galac- and QGSJET-II [14] interaction models. About 10−2 tic Center [8]. The factor ∼10 improvement in γ-ray of these showers trigger the array, and due to the ex- flux sensitivity of H.E.S.S. over previous generation ex- tremelyefficientbackgroundrejection,only10−6fallinto periments is based largely on superior rejection of the the regime ζ >0.9. While a componentof heaviernuclei hadronic background. Because this measurement does isrequiredtoexplainthedistributionofζ atvaluesupto not discriminate between electrons and positrons, elec- 0.5,thebackgroundcanbeconsideredaspurelyprotonic trons is used generically in the following to refer to both at larger values of ζ. particle and anti-particle. The H.E.S.S. electron analy- sis presented here is based on the selection of electron- Fig. 1 shows the measured distribution of the param- 3 initiatedairshowersareinpracticeextremelydifficultto s 900 nt separate from γ-ray showers, the peak in our data at Eve 800 106 120 HESS 1-4 TeV ζ = 1 may contain a contribution from γ-ray showers. 100 Electrons The signal measured by H.E.S.S. (close to ζ = 1) is 105 700 80 Protons therefore a combinationof the CR electron flux (CREF) 104 Best Fit Model and the extragalactic γ-ray background (EGRB). The 60 600 level of the EGRB lies many orders of magnitude below 103 40 the CREF at GeV energies but a naive extrapolation of 500 102 20 the lastfew data points measuredby EGRET [15]yields an dN/dE ∝ E−2 spectrum which reaches the level of 0 400 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 the CREF at a few TeV. However, most models for the EGRB yield TeV fluxes at least one order of magnitude 300 lowerthanthisextrapolation(seeforexample[16]). The predicted flux of inverse Compton scattered solar pho- 200 tons off CR electrons is also negligible due to our geom- etry pointing away from the Sun [17]. Given the uncer- 100 tainty in the EGRB/CREF ratio at TeV energies it is desirable to separate electrons and γ-rays in our data. 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 ζ Essentially the only useful separation parameter is the depth of shower maximum (Xmax), which occurs on av- erage ≈20 gcm−2 (or ∼ half a radiation length) higher FIG.1: Themeasured distributionoftheparameter ζ,com- in the atmosphere for electrons. Fig. 2 compares recon- pared with distributions forsimulated protonsand electrons, for showers with reconstructed energy between 1 and 4 TeV. structed Xmax distributions for simulated protons, elec- The best fit model combination of electrons and protons is trons and γ-rays to the experimentally measured Xmax shown as a shaded band. The proton simulations use the distributionforelectron-likeevents(ζ >0.9). Afitofthe SIBYLL hadronic interaction event generator. The left inset Xmax distribution with the electron/γ-ray fraction as a showsthecompletedistributionfromzerotoonewithentries freeparameterresultsinamaximum10%contributionof on a log scale; the data are shown as points, the filled his- γ-raystothesignal(foraconfidencelevelof90%),which togram shows a mixed composition (proton, He, N, Si & Fe) cosmic-ray model. To demonstrate the match between sim- is supported by the displacement between the Xmax dis- ulation and data in electromagnetic showers, the right inset tributions from data used for this electron analysis and shows background subtracted γ-ray data as points and γ-ray data from a γ-ray rich data set (inset of Fig. 2). How- simulations as filled histogram. ever, taking into account a conservative systematic un- certainty in the determination of Xmax of 5 gcm−2 due eter ζ compared with the simulated distributions for the to atmospheric uncertainties, we cannot exclude a sig- energy range 1–4 TeV. The peak close to ζ = 1 is ev- nificantcontaminationof≈50%ofourelectronmeasure- idence of a diffuse component of purely-electromagnetic mentbythediffuseextragalacticγ-raybackground. Sys- showers at these energies. The data at ζ > 0.6 can be tematic uncertainties in the hadronic modeling are not described by a combination of simulated electrons and considered. protons. By fitting the ζ distribution of the data with Fig. 3 shows the CR electron spectrum derived from thedistributionsofsimulatedelectronsandprotonsinin- this analysis together with a compilation of earlier dependentenergybands(withtwofreeparametersbeing measurements. Systematic errors on the reconstructed the electron and proton contribution), the most proba- spectrum arise from uncertainties in the simulation of ble number of measured electron showers in each energy hadronicinteractionsandtheatmosphericmodel,aswell band can be deduced. The total normalized goodness- as in the absolute energy scale. The energy scale un- of-fit in the ζ range of 0.6–1 for reconstructed energies certainty is ≈15% and is illustrated by a double arrow between 1 and 4 TeV is χ2/ν = 0.98 for a model of in Fig. 3. The uncertainty arising from the subtrac- simulated electrons and protons using SIBYLL (proba- tion of the hadronic background has been estimated by bility p = 0.5) and 2.15 for a model using QGSJET-II comparison of the spectra obtained using the SIBYLL (p = 1.7 × 10−4),whichdemonstratesthattheSIBYLL and QGSJET-II models. The ζ distributions for pro- modelprovidesabetterdescriptionofmeasurableparam- tons show a slight rise toward ζ = 1 (see Fig. 1), pre- eters of air showersinitiated by protons of TeV energies. sumably reflecting events where a large fraction of pro- 0 Coupled with the knowledge ofthe energy-dependentef- ton energy is transformed to a single π . The rise is fective collection area, which is obtained from electron somewhatmore pronouncedfor SIBYLL as comparedto simulationsfollowingapowerlawwithaspectralindexof QGSJET-II, giving rise to the model dependence. Ar- 3.3,thenumberofmeasuredelectronshowerscanbeused tificially doubling the γ-ray like component in SIBYLL todeterminetheprimaryelectronspectrum. Aselectron- reduces the electron flux by ∼ 20%, without significant 4 due to the limited energy range no conclusion can be s nt700 800 drawnconcerningtheexistenceofastepinthespectrum e v as claimed by ATIC. E 600 600 400 1) -r 500 s 200 -1 s 2 -m 400 0200 300 400 500 2 ∆ E ± 15% V e Data e γ Data G 300 Electrons E ( d Gammas N/102 p+e Model d 200 p+γ Model 3 E AMS 100 HEAT HEAT 94-95 BETS PPB-BETS Kobayashi 0 200 250 300 350 400 450 500 550 ATIC HESS X - 93 log(E/1 TeV) (g cm-2) (systematic error) max (Fit A) (Fit B) FIG. 2: The distribution of reconstructed shower maximum (Xmax) for H.E.S.S. data, compared to simulations. For 1 10 102 103 104 each shower the measured Xmax is corrected for the energy Energy (GeV) dependent shower elongation (93 gcm−2/decade is the re- constructed elongation rate expected for electron primaries). FIG. 3: The energy spectrum E3 dN/dE of CR electrons as Showerswithreconstructedenergiesbetween1and4TeVare measured by H.E.S.S. in comparison with previous measure- included. The bands show the combination of electrons and ments. The H.E.S.S. data are shown as solid points. The protons(simulatedusingSIBYLL)andofγ-raysandprotons, two fit functions (A and B) are described in the main text. with a ratio determined by a fit to the ζ distribution of the The shaded band indicates the approximate systematic er- data in this energy range. The distributions of electrons and ror arising from uncertainties in the modeling of hadronic γ-rays are shown for comparison. The inset contains a com- interactions and in the atmospheric model. The double ar- parison of this data (black) with a γ-ray rich data set taken row indicates the effect of an energy scale shift of 15%, the from regions <0.15◦ from γ-ray sources (gray). approximate systematic uncertainty on the H.E.S.S. points. Previous data are reproduced from: AMS [18], HEAT [19], change in spectral shape. Detailed tests of the analy- HEAT94-95 [20], BETS [21],PPB-BETS [22], Kobayashi[2] sis using different zenith angle ranges, different analysis and ATIC [23]. cuts (variations of the cuts on ζ, the maximum impact Whilst the detailed interpretation of this result is be- distance of the showers and the minimal intensity of the yond the scope of this paper, we note that our measure- showerimageinthecamera),differentregionsinthesky, ment implies the existence of at least one source of CR different seasons and years as well as another fitting al- electronsinthelocalGalaxy(within∼1kpc). Somesce- gorithm all yield consistent results. The estimated sys- narios of a strong local source [2] are excluded. This tematic errors,apartfromthe 15%scaleuncertainty,are measurement is the first ground-based measurement of illustrated by the shaded band in Fig. 3. Our data are CR electrons. Future IACT arrays with effective areas welldescribedbyapower-law: dN/dE = k(E/1TeV)−Γ beyond106 m2 shouldbe ableto extendthe spectrumto with k = (1.17±0.02) × 10−4 TeV−1m−2sr−1s−1 and 10 TeV using this technique. Γ = 3.9± 0.1 (stat) (χ2/ν = 3.6, p = 10−3, Fit A), The support of the Namibian authorities and of the which implies a steepening of the spectrum compared to UniversityofNamibiainfacilitatingtheconstructionand GeVenergies. The spectralindex showslittle modeland operationofH.E.S.S.isgratefullyacknowledged,asisthe sample dependence, resulting in ∆Γ(syst.) . 0.3. At support by the German Ministry for Education and Re- lower energies the flux reported here is somewhat higher search(BMBF),theMaxPlanckSociety,theFrenchMin- thanpreviousresults,butfullyconsistentwithinthe15% istryfor Research,the CNRS-IN2P3andthe Astroparti- scale error. Leaving the scale factor free, H.E.S.S. data cle Interdisciplinary Programme of the CNRS, the U.K. combined with earlier electron data are well reproduced Science and Technology Facilities Council (STFC), the by an exponentially cutoff powerlaw with an index of IPNP of the Charles University, the Polish Ministry of −3.05± 0.02 and a cutoff at 2.1± 0.3 TeV, combined Science and Higher Education, the South African De- with a scale adjustment of −11% (Fit B). H.E.S.S. data partment of Science and Technology and National Re- arealsocompatiblewithveryrecentATICdata[23],but search Foundation, and by the University of Namibia. 5 Weappreciatetheexcellentworkofthetechnicalsupport [9] L. Breiman & A. Cutler, staffinBerlin,Durham,Hamburg,Heidelberg,Palaiseau, http://www.stat.berkeley.edu/users/breiman/RandomForests/ Paris,Saclay,andinNamibiaintheconstructionandop- [10] R. K. Bock et al., Nuclear Instruments and Methods in Physical Research A516, 511 (2004). eration of the equipment. [11] A. Hillas, Proceedings 19th International Cosmic Ray Conference, La Jolla, F. C. Jones, 3, 445 (1985). [12] D. Heck et al., Forschungszentrum Karlsruhe Report FZKA 6019 (1998). [13] R. S. Fletcher, T. K. Gaisser, P. Lipari, & T. Stanev, ∗ supportedbyCAPESFoundation,MinistryofEducation Phys. Rev.D 50, 5710 (1994). of Brazil [14] S. Ostapchenko et al., Proceedings 29th International † Electronic address: [email protected] Cosmic Ray Conference, Pune, Tata Institute of Fun- ‡ Electronic address: [email protected] damental Research, 7, 135 (2005). § UMR7164(CNRS,Universit´eParisVII,CEA,Observa- [15] A.W.Strong,I.V.Moskalenko&O.Reimer,Astrophys. toire deParis) J., 613, 956 (2004). [1] F. A. Aharonian, A. M. Atoyan, H. J. V¨olk, Astron. & [16] P.S. Coppi & F. A. Aharonian, Astrophys. J., 487, L9 Astrophys.,294, L41 (1995). (1997). [2] T. Kobayashi et al.,Astrophys.J., 601, 340 (2004). [17] I. V. Moskalenko, T. A. Porter, S. W. Digel, Astrophys. [3] D.Mu¨ller, Adv.SpaceRes., 27, 659 (2001). J., 652, L65 (2006). [4] J.Nishimura,Proc.TowardsaMajorCherenkovDetector [18] M. Aguilar et al., Physics Reports366, 331 (2002). III,Universal Academy Press, Tokyo, page 1 (1994). [19] S. W. Barwick et al.,Astrophys.J., 498, 779 (1998). [5] J.A.Hinton(H.E.S.S.Collaboration),NewAstron.Rev. [20] M. A.DuVernoiset al., Astrophys.J., 559, 296 (2001). 48, 331 (2004). [21] S. Torii et al.,Astrophys.J., 559, 973 (2001). [6] F. A.Aharonian et al.,Nature 432, 75 (2004). [22] S. Torii et al.,arXiv:0809.0760 (2008). [7] F. A. Aharonian et al., Astron. & Astrophys. 437, L7 [23] J. Chang et al.,Nature, 456, 362-365 (2008). (2005). [8] F. A.Aharonian et al.,Nature 439, 695 (2006).