Measurement of the Depth of Maximum of Extensive Air Showers above 10^18 eV
aa r X i v : . [ a s t r o - ph . H E ] F e b Measurement of the Depth of Maximum of Extensive Air Showers above 10 eV (The Pierre Auger Collaboration)J. Abraham, P. Abreu, M. Aglietta, E.J. Ahn, D. Allard, I. Allekotte, J. Allen, J. Alvarez-Mu˜niz, M. Ambrosio, L. Anchordoqui, S. Andringa, T. Antiˇci´c, A. Anzalone, C. Aramo, E. Arganda, K. Arisaka, F. Arqueros, H. Asorey, P. Assis, J. Aublin, M. Ave,
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Ziolkowski National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina LIP and Instituto Superior T´ecnico, Lisboa, Portugal Istituto di Fisica dello Spazio Interplanetario (INAF),Universit`a di Torino and Sezione INFN, Torino, Italy Fermilab, Batavia, IL, USA Laboratoire AstroParticule et Cosmologie (APC),Universit´e Paris 7, CNRS-IN2P3, Paris, France Centro At´omico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina New York University, New York, NY, USA Universidad de Santiago de Compostela, Spain Universit`a di Napoli “Federico II” and Sezione INFN, Napoli, Italy University of Wisconsin, Milwaukee, WI, USA Rudjer Boˇskovi´c Institute, 10000 Zagreb, Croatia Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy Universidad Complutense de Madrid, Madrid, Spain University of California, Los Angeles, CA, USA Laboratoire de Physique Nucl´eaire et de Hautes Energies (LPNHE),Universit´es Paris 6 et Paris 7, CNRS-IN2P3, Paris, France Karlsruhe Institute of Technology - Campus North - Institut f¨ur Kernphysik, Karlsruhe, Germany University of Chicago, Enrico Fermi Institute, Chicago, IL, USA Pierre Auger Southern Observatory and Comisi´on Nacional de Energ´ıa At´omica, Malarg¨ue, Argentina Universit¨at Siegen, Siegen, Germany IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina Karlsruhe Institute of Technology - Campus North - Institut f¨ur Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany University of Adelaide, Adelaide, S.A., Australia Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil Universidade Estadual do Sudoeste da Bahia, Vitoria da Conquista, BA, Brazil Ohio State University, Columbus, OH, USA Colorado State University, Fort Collins, CO, USA University of New Mexico, Albuquerque, NM, USA Bergische Universit¨at Wuppertal, Wuppertal, Germany Laboratoire de Physique Subatomique et de Cosmologie (LPSC),Universit´e Joseph Fourier, INPG, CNRS-IN2P3, Grenoble, France University of Wisconsin, Madison, WI, USA Max-Planck-Institut f¨ur Radioastronomie, Bonn, Germany Universidad de Alcal´a, Alcal´a de Henares (Madrid), Spain Dipartimento di Fisica dell’Universit`a del Salento and Sezione INFN, Lecce, Italy Karlsruhe Institute of Technology - Campus South - Institut f¨ur Experimentelle Kernphysik (IEKP), Karlsruhe, Germany Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic Universit`a di Roma II “Tor Vergata” and Sezione INFN, Roma, Italy Institute of Nuclear Physics PAN, Krakow, Poland Colorado State University, Pueblo, CO, USA School of Physics and Astronomy, University of Leeds, United Kingdom Universidad de Granada & C.A.F.P.E., Granada, Spain Case Western Reserve University, Cleveland, OH, USA Universit`a di Catania and Sezione INFN, Catania, Italy Universit`a di Torino and Sezione INFN, Torino, Italy Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil Centro At´omico Constituyentes (Comisi´on Nacional de Energ´ıa At´omica/CONICET/UTN-FRBA), Buenos Aires, Argentina Pierre Auger Southern Observatory, Malarg¨ue, Argentina IMAPP, Radboud University, Nijmegen, Netherlands NIKHEF, Amsterdam, Netherlands Laboratoire de l’Acc´el´erateur Lin´eaire (LAL), Universit´e Paris 11, CNRS-IN2P3, Orsay, France Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico Pennsylvania State University, University Park, PA, USA Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia SUBATECH, CNRS-IN2P3, Nantes, France Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico Universit`a di Milano and Sezione INFN, Milan, Italy Universidade Federal do Rio de Janeiro, Instituto de F´ısica, Rio de Janeiro, RJ, Brazil Universidade de S˜ao Paulo, Instituto de F´ısica, S˜ao Carlos, SP, Brazil Kernfysisch Versneller Instituut, University of Groningen, Groningen, Netherlands Institut de Physique Nucl´eaire d’Orsay (IPNO),Universit´e Paris 11, CNRS-IN2P3, Orsay, France RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany Michigan Technological University, Houghton, MI, USA Pontif´ıcia Universidade Cat´olica, Rio de Janeiro, RJ, Brazil Institute for Nuclear Science and Technology (INST), Hanoi, Vietnam University of Hawaii, Honolulu, HI, USA ASTRON, Dwingeloo, Netherlands J. Stefan Institute, Ljubljana, Slovenia Dipartimento di Fisica dell’Universit`a and INFN, Genova, Italy University of L´od´z, L´od´z, Poland Louisiana State University, Baton Rouge, LA, USA Universidade de S˜ao Paulo, Instituto de F´ısica, S˜ao Paulo, SP, Brazil INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy Departamento de F´ısica, FCEyN, Universidad de Buenos Aires y CONICET, Argentina Universidade Estadual de Feira de Santana, Brazil Palack´y University, Olomouc, Czech Republic Universit`a dell’Aquila and INFN, L’Aquila, Italy Universit¨at Hamburg, Hamburg, Germany Universidade Federal do ABC, Santo Andr´e, SP, Brazil Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico Dipartimento di Ingegneria dell’Innovazione dell’Universit`a del Salento and Sezione INFN, Lecce, Italy Southern University, Baton Rouge, LA, USA Charles University, Faculty of Mathematics and Physics,Institute of Particle and Nuclear Physics, Prague, Czech Republic Centro de Investigaciones en L´aseres y Aplicaciones, CITEFA and CONICET, Argentina Instituto de F´ısica Corpuscular, CSIC-Universitat de Val`encia, Valencia, Spain Northeastern University, Boston, MA, USA Caltech, Pasadena, USA Universidade Federal da Bahia, Salvador, BA, Brazil University of Nebraska, Lincoln, NE, USA Gran Sasso Center for Astroparticle Physics, Italy Instituto de Astronom´ıa y F´ısica del Espacio (CONICET), Buenos Aires, Argentina Instituto Nacional de Astrofisica, Optica y Electronica, Puebla, Mexico Colorado School of Mines, Golden, CO, USA Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdom Argonne National Laboratory, Argonne, IL, USA Universit`a di Palermo and Sezione INFN, Catania, Italy Konan University, Kobe, Japan Centro de Investigaci´on y de Estudios Avanzados del IPN (CINVESTAV), M´exico, D.F., Mexico (Dated: October 24, 2018)
We describe the measurement of the depth of maximum, X max , of the longitudinal developmentof air showers induced by cosmic rays. Almost four thousand events above 10 eV observed bythe fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surfacedetector station are selected for the analysis. The average shower maximum was found to evolve withenergy at a rate of (106 +35 − ) g/cm /decade below 10 . ± . eV and (24 ±
3) g/cm /decade abovethis energy. The measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm . Theinterpretation of these results in terms of the cosmic ray mass composition is briefly discussed. PACS numbers: 96.50.sd,13.85.Tp,98.70.Sa
Introduction – The energy dependence of the masscomposition of cosmic rays is, along with the flux and ar-rival direction distribution, an important parameter forthe understanding of the sources and propagation of cos-mic rays at very high energy. There are several modelsthat describe the observed flux of cosmic rays very well,but each of these models has different assumptions aboutthe cosmic ray sources and correspondingly predicts adifferent mass composition at Earth. For example, thehardening of the cosmic ray energy spectrum at ener-gies between 10 eV and 10 eV, known as the ’ankle’,is presumed to be either a signature of the transitionfrom galactic to extragalactic cosmic rays or a distor-tion of a proton-dominated extragalactic spectrum dueto energy losses [1]. Moreover, composition informationmay eventually help to decide whether the flux suppres-sion observed above 4 · eV [2] is due mainly to the in-teraction of cosmic rays with the microwave backgroundor a signature of the maximum injection energy of thesources [3].Due to the low flux at these energies, the compositionof cosmic rays cannot be measured directly, but has tobe inferred from observations of extensive air showers.The atmospheric depth, X max , at which the longitudinaldevelopment of a shower reaches its maximum in termsof the number of secondary particles is correlated withthe mass of the incident cosmic ray particle. With thegeneralization of Heitler’s model of electron-photon cas-cades to hadron-induced showers and the superpositionassumption for nuclear primaries of mass A , the averagedepth of the shower maximum, h X max i , at a given energy E is expected to follow [4] h X max i = α (ln E − h ln A i ) + β, ) (1)where h ln A i is the average of the logarithm of the pri-mary masses. The coefficients α and β depend on thenature of hadronic interactions, most notably on the mul-tiplicity, elasticity and cross-section in ultra-high energycollisions of hadrons with air, see e.g. [5]. AlthoughEq. (1) is based on a simplified description of air showers,it gives a good description of air shower simulations withenergy-independent parameters α and β in the energyrange considered here, see [6]. Only physics processesnot accounted for in currently available interaction mod-els could lead to a significant energy dependence of theseparameters. The change of h X max i per decade of energy is called elongation rate [7], D = d h X max i d lg E ≈ α (cid:18) − d h ln A i d ln E (cid:19) ln(10) , (2)and it is sensitive to changes in composition with en-ergy. A complementary composition-dependent observ-able is the magnitude of the shower-to-shower fluctua-tions of the depth of maximum, RMS( X max ), which isexpected to decrease with the number of primary nucle-ons A (though not as fast as 1 / √ A [8]) and to increasewith the interaction length of the primary particle.At ultra high energies, the shower maximum can beobserved directly with fluorescence detectors. Previouslypublished X max measurements [9, 10] focused mainly on h X max i as a function of energy and had only limitedstatistics above 10 eV.Here we present a measurement of both h X max i andRMS( X max ) using high quality and high statistics datacollected with the southern site of the Pierre Auger Ob-servatory [11]. The Observatory is located in the provinceof Mendoza, Argentina and consists of two detectors.The surface detector (SD) array comprises 1600 water-Cherenkov detectors arranged on a triangular grid with1500 m spacing that cover an area of over 3000 km . Thewater-Cherenkov detectors are sensitive to the air showercomponents at ground level. The fluorescence detector(FD) consists of 24 optical telescopes overlooking the ar-ray, which can observe the longitudinal shower develop-ment by detecting the fluorescence and Cherenkov lightproduced by charged particles along the shower trajec-tory in the atmosphere. Data Analysis. – This work is based on air shower datarecorded between December 2004 and March 2009. Onlyevents detected in hybrid mode [12] are considered, i.e.the shower development must have been measured by theFD, and at least one coincident SD station is required toprovide a ground-level time. Using the time constraintfrom the SD, the shower geometry can be determinedwith an angular uncertainty of 0.6 ◦ [13]. The longitu-dinal profile of the energy deposit is reconstructed [14]from the light recorded by the FD using the fluorescenceand Cherenkov yields and lateral distributions from [15].With the help of data from atmospheric monitoring de-vices [16] the light collected by the telescopes is correctedfor the attenuation between the shower and the detector ] [g/cm2/ max X ∆ −80 −60 −40 −20 0 20 40 60 80 e n t r i es data ± RMS = 20 MC (syst.) g/cm +2 −1 RMS = 19
E [eV] ] r es o l u t i on [ g / c m m ax X ± MC FIG. 1: Difference between X max measured in showers simul-taneously at two FD stations ( h lg( E/ eV) i = 19 . X max resolution is displayed as a function of energy in the inset. and the longitudinal shower profile is reconstructed asa function of atmospheric depth. X max is determinedby fitting the reconstructed longitudinal profile with aGaisser-Hillas function [17].An unbiased set of high quality events is selected withthe statistical uncertainty of the reconstructed X max be-ing comparable to the size of the fluctuations expectedfor nuclei as heavy as iron ( ≈
20 g/cm ) and small sys-tematic uncertainties as explained in the following.The impact of varying atmospheric conditions on the X max measurement is minimized by rejecting time peri-ods with cloud coverage and by requiring reliable mea-surements of the vertical optical depth of aerosols. Pro-files that are distorted by residual cloud contaminationare rejected by a loose cut on the quality of the profilefit ( χ /Ndf < eV where the probability for at leastone triggered SD station is 100%, irrespective of the massof the primary particle [18]. The geometrical reconstruc-tion of showers with a large apparent angular speed of theimage in the telescope is susceptible to uncertainties inthe time synchronization between FD and SD. Therefore,events with a light emission angle towards the FD thatis smaller than 20 ◦ are rejected. This cut also removesevents with a large fraction of Cherenkov light. The en-ergy and shower maximum can be reliably measured onlyif X max is in the field of view (FOV) of the telescopes(covering 1 . ◦ to 30 ◦ in elevation). Events for which onlythe rising or falling edge of the profile is detected arenot used. Moreover, we calculate the expected statisti-cal uncertainty of the reconstruction of X max for eachevent, based on the shower geometry and atmosphericconditions, and require it to be better than 40 g/cm .The latter two selection criteria may cause a selectionbias due to a systematic undersampling of the tails ofthe true X max distribution, since showers developing very E [eV] ] > [ g / c m m ax < X Auger 09 HiRes ApJ05 broken line fit sys. ± FIG. 2: h X max i as a function of energy. Lines denote a fitwith a broken line in lg E . The systematic uncertainties of h X max i are indicated by a dashed line. The number of eventsin each energy bin is displayed below the data points. HiResdata [10] are shown for comparison. deep or shallow in the atmosphere might be rejected fromthe data sample. To avoid such a bias in the measured h X max i and RMS( X max ) we apply fiducial volume cutsbased on the shower geometry that ensure that the view-able X max range for each shower is large enough to ac-commodate the full X max distribution [19].After all cuts, 3754 events are selected for the X max analysis. The X max resolution as a function of energyfor these events is estimated using a detailed simulationof the FD and the atmosphere. As shown in the insetof Fig. 1, the resolution is at the 20 g/cm level above afew EeV. The difference between the reconstructed X max values in events that had a sufficiently high energy tobe detected independently by two or more FD stationsis used to cross-check these findings. As can be seen inFig. 1, the simulations reproduce the data well. Results and Discussion. – The measured h X max i andRMS( X max ) values are shown in Figs. 2 and 3. We usebins of ∆ lg E = 0 . E = 0 . . eV, integratingup to the highest energy event ( E = (59 ±
8) EeV). Thesystematic uncertainty of the FD energy scale is 22% [18].Uncertainties of the calibration, atmospheric conditions,reconstruction and event selection give rise to a system-atic uncertainty of ≤
13 g/cm for h X max i and ≤ for the RMS. The results were found to be independentof zenith angle, time periods and FD stations within theexperimental uncertainties.A fit of the measured h X max i values with a con-stant elongation rate does not describe our data( χ /Ndf=34.9/11), but as can be seen in Fig. 2, us-ing two slopes yields a satisfactory fit ( χ /Ndf=9.7/9)with an elongation rate of (106 +35 − ) g/cm /decade below10 . ± . eV and (24 ±
3) g/cm /decade above this en- E [eV] ] > [ g / c m m ax < X p r o t o n i r o n QGSJET01QGSJETIISibyll2.1EPOSv1.99
E [eV] ] ) [ g / c m m ax R M S ( X protoniron FIG. 3: h X max i and RMS( X max ) compared with air shower simulations [20] using different hadronic interaction models[21]. ergy. If the properties of hadronic interactions do notchange significantly over less than two orders of magni-tude in primary energy ( < factor 10 in center of massenergy), this change of ∆ D =(82 +35 − ) g/cm /decadewould imply a change in the energy dependence of thecomposition around the ankle, supporting the hypothe-sis of a transition from galactic to extragalactic cosmicrays in this region.The h X max i result of this analysis is compared to theHiRes data [10] in Fig. 2. Both data-sets agree wellwithin the quoted systematic uncertainties. The χ / Ndfof the HiRes data with respect to the broken-line fit de-scribed above is 20 . /