Measurement of the Depth of Maximum of Extensive Air Showers above1018  eV

PUBLISHED VERSION Abraham, J.;...; Barber, Kerridwen Bette; Barbosa, A. F.;...; Cooper, Matthew John; Coppens, J.;...; Dawson, Bruce Robert; de Almeida, R. M.;...; Holmes, Vanessa Catherine; ... et al.; Pierre Auger Collaboration Measurement of the depth of maximum of extensive air showers above 10¹⁸ eV Physical Review Letters, 2010; 104(9):091101 ©2010 American Physical Society http://link.aps.org/doi/10.1103/PhysRevLett.104.091101 PERMISSIONS http://publish.aps.org/authors/transfer-of-copyright-agreement http://link.aps.org/doi/10.1103/PhysRevD.62.093023 “The author(s), and in the case of a Work Made For Hire, as defined in the U.S. Copyright Act, 17 U.S.C. §101, the employer named [below], shall have the following rights (the “Author Rights”): [...] 3. The right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website and to make copies of all or part of the Article, including the APS-prepared version without revision or modification, for the author(s)’ and/or the employer’s use for educational or research purposes.” 13th May 2013 http://hdl.handle.net/2440/61284 PRL 104, 091101 (2010) PHYSICAL REVIEW LETTERS week ending 5 MARCH 2010 Measurement of the Depth of Maximum of Extensive Air Showers above 1018 eV J. Abraham,1 P. Abreu,2 M. Aglietta,3 E. J. Ahn,4 D. Allard,5 I. Allekotte,6 J. Allen,7 J. Alvarez-Muñiz,8 M. Ambrosio,9 L. Anchordoqui,10 S. Andringa,2 T. Antičić,11 A. Anzalone,12 C. Aramo,9 E. Arganda,13 K. Arisaka,14 F. Arqueros,13 H. Asorey,6 P. Assis,2 J. Aublin,15 M. Ave,16,17 G. Avila,18 T. Bäcker,19 D. Badagnani,20 M. Balzer,21 K. B. Barber,22 A. F. Barbosa,23 S. L. C. Barroso,24 B. Baughman,25 P. Bauleo,26 J. J. Beatty,25 B. R. Becker,27 K. H. Becker,28 A. Bellétoile,29 J. A. Bellido,22 S. BenZvi,30 C. Berat,29 T. Bergmann,21 X. Bertou,6 P. L. Biermann,31 P. Billoir,15 O. Blanch-Bigas,15 F. Blanco,13 M. Blanco,32 C. Bleve,33 H. Blümer,34,16 M. Boháčová,17,35 D. Boncioli,36 C. Bonifazi,15 R. Bonino,3 N. Borodai,37 J. Brack,26 P. Brogueira,2 W. C. Brown,38 R. Bruijn,39 P. Buchholz,19 A. Bueno,40 R. E. Burton,41 N. G. Busca,5 K. S. Caballero-Mora,34 L. Caramete,31 R. Caruso,42 A. Castellina,3 O. Catalano,12 G. Cataldi,33 L. Cazon,2,17 R. Cester,43 J. Chauvin,29 A. Chiavassa,3 J. A. Chinellato,44 A. Chou,4,7 J. Chudoba,35 R. W. Clay,22 E. Colombo,45 M. R. Coluccia,33 R. Conceição,2 F. Contreras,46 H. Cook,39 M. J. Cooper,22 J. Coppens,47,48 A. Cordier,49 U. Cotti,50 S. Coutu,51 C. E. Covault,41 A. Creusot,52 A. Criss,51 J. Cronin,17 A. Curutiu,31 S. Dagoret-Campagne,49 R. Dallier,53 K. Daumiller,16 B. R. Dawson,22 R. M. de Almeida,44 M. De Domenico,42 C. De Donato,54,55 S. J. de Jong,47 G. De La Vega,1 W. J. M. de Mello Junior,44 J. R. T. de Mello Neto,56 I. De Mitri,33 V. de Souza,57 K. D. de Vries,58 G. Decerprit,5 L. del Peral,32 O. Deligny,59 A. Della Selva,9 C. Delle Fratte,36 H. Dembinski,60 C. Di Giulio,36 J. C. Diaz,61 M. L. Dı́az Castro,62 P. N. Diep,63 C. Dobrigkeit,44 J. C. D’Olivo,54 P. N. Dong,63,59 A. Dorofeev,26 J. C. dos Anjos,23 M. T. Dova,20 D. D’Urso,9 I. Dutan,31 M. A. DuVernois,64 J. Ebr,35 R. Engel,16 M. Erdmann,60 C. O. Escobar,44 A. Etchegoyen,45 P. Facal San Luis,17,8 H. Falcke,47,65 G. Farrar,7 A. C. Fauth,44 N. Fazzini,4 A. Ferrero,45 B. Fick,61 A. Filevich,45 A. Filipčič,66,52 I. Fleck,19 S. Fliescher,60 C. E. Fracchiolla,26 E. D. Fraenkel,58 U. Fröhlich,19 W. Fulgione,3 R. F. Gamarra,45 S. Gambetta,67 B. Garcı́a,1 D. Garcı́a Gámez,40 D. Garcia-Pinto,13 X. Garrido,16,49 G. Gelmini,14 H. Gemmeke,21 P. L. Ghia,59,3 U. Giaccari,33 M. Giller,68 H. Glass,4 L. M. Goggin,10 M. S. Gold,27 G. Golup,6 F. Gomez Albarracin,20 M. Gómez Berisso,6 P. Gonçalves,2 D. Gonzalez,34 J. G. Gonzalez,40,69 D. Góra,34,37 A. Gorgi,3 P. Gouffon,70 S. R. Gozzini,39 E. Grashorn,25 S. Grebe,47 M. Grigat,60 A. F. Grillo,71 Y. Guardincerri,72 F. Guarino,9 G. P. Guedes,73 J. D. Hague,27 V. Halenka,74 P. Hansen,20 D. Harari,6 S. Harmsma,58,48 J. L. Harton,26 A. Haungs,16 T. Hebbeker,60 D. Heck,16 A. E. Herve,22 C. Hojvat,4 V. C. Holmes,22 P. Homola,37 J. R. Hörandel,47 A. Horneffer,47 M. Hrabovský,74,35 T. Huege,16 M. Hussain,52 M. Iarlori,75 A. Insolia,42 F. Ionita,17 A. Italiano,42 S. Jiraskova,47 K. Kadija,11 M. Kaducak,4 K. H. Kampert,28 T. Karova,35 P. Kasper,4 B. Kégl,49 B. Keilhauer,16 A. Keivani,69 J. Kelley,47 E. Kemp,44 R. M. Kieckhafer,61 H. O. Klages,16 M. Kleifges,21 J. Kleinfeller,16 R. Knapik,26 J. Knapp,39 D.-H. Koang,29 A. Krieger,45 O. Krömer,21 D. Kruppke-Hansen,28 F. Kuehn,4 D. Kuempel,28 K. Kulbartz,76 N. Kunka,21 A. Kusenko,14 G. La Rosa,12 C. Lachaud,5 B. L. Lago,56 P. Lautridou,53 M. S. A. B. Leão,77 D. Lebrun,29 P. Lebrun,4 J. Lee,14 M. A. Leigui de Oliveira,77 A. Lemiere,59 A. Letessier-Selvon,15 I. Lhenry-Yvon,59 R. López,78 A. Lopez Agüera,8 K. Louedec,49 J. Lozano Bahilo,40 A. Lucero,3 M. Ludwig,34 H. Lyberis,59 M. C. Maccarone,12 C. Macolino,15,75 S. Maldera,3 D. Mandat,35 P. Mantsch,4 A. G. Mariazzi,20 V. Marin,53 I. C. Maris,15,34 H. R. Marquez Falcon,50 G. Marsella,79 D. Martello,33 O. Martı́nez Bravo,78 H. J. Mathes,16 J. Matthews,69,80 J. A. J. Matthews,27 G. Matthiae,36 D. Maurizio,43 P. O. Mazur,4 M. McEwen,32 G. Medina-Tanco,54 M. Melissas,34 D. Melo,43 E. Menichetti,43 A. Menshikov,21 C. Meurer,60 S. Mičanović,11 M. I. Micheletti,45 W. Miller,27 L. Miramonti,55 S. Mollerach,6 M. Monasor,17,13 D. Monnier Ragaigne,49 F. Montanet,29 B. Morales,54 C. Morello,3 E. Moreno,78 J. C. Moreno,20 C. Morris,25 M. Mostafá,26 S. Mueller,16 M. A. Muller,44 R. Mussa,43 G. Navarra,3,* J. L. Navarro,40 S. Navas,40 P. Necesal,35 L. Nellen,54 P. T. Nhung,63 N. Nierstenhoefer,28 D. Nitz,61 D. Nosek,81 L. Nožka,35 M. Nyklicek,35 J. Oehlschläger,16 A. Olinto,17 P. Oliva,28 V. M. Olmos-Gilbaja,8 M. Ortiz,13 N. Pacheco,32 D. Pakk Selmi-Dei,44 M. Palatka,35 J. Pallotta,82 N. Palmieri,34 G. Parente,8 E. Parizot,5 S. Parlati,71 A. Parra,8 J. Parrisius,34 R. D. Parsons,39 S. Pastor,83 T. Paul,84 V. Pavlidou,17,85 K. Payet,29 M. Pech,35 J. Pe˛kala,37 R. Pelayo,8 I. M. Pepe,86 L. Perrone,79 R. Pesce,67 E. Petermann,87 S. Petrera,75,88 P. Petrinca,36 A. Petrolini,67 Y. Petrov,26 J. Petrovic,48 C. Pfendner,30 R. Piegaia,72 T. Pierog,16 M. Pimenta,2 V. Pirronello,42 M. Platino,45 V. H. Ponce,6 M. Pontz,19 P. Privitera,17 M. Prouza,35 E. J. Quel,82 J. Rautenberg,28 O. Ravel,53 D. Ravignani,45 A. Redondo,32 B. Revenu,53 F. A. S. Rezende,23 J. Ridky,35 S. Riggi,42 M. Risse,19,28 P. Ristori,82 C. Rivière,29 V. Rizi,75 C. Robledo,78 G. Rodriguez,8,36 J. Rodriguez Martino,46,42 J. Rodriguez Rojo,46 I. Rodriguez-Cabo,8 M. D. Rodrı́guez-Frı́as,32 G. Ros,32 J. Rosado,13 T. Rossler,74 M. Roth,16 B. Rouillé-d’Orfeuil,17,5 E. Roulet,6 A. C. Rovero,89 F. Salamida,16,75 H. Salazar,78,90 G. Salina,36 F. Sánchez,45,54 M. Santander,46 C. E. Santo,2 E. Santos,2 E. M. Santos,56 F. Sarazin,91 S. Sarkar,92 R. Sato,46 N. Scharf,60 V. Scherini,28,69 0031-9007=10=104(9)=091101(7) 091101-1 Ó 2010 The American Physical Society PRL 104, 091101 (2010) PHYSICAL REVIEW LETTERS week ending 5 MARCH 2010 H. Schieler,16 P. Schiffer,60 A. Schmidt,21 F. Schmidt,17 T. Schmidt,34 O. Scholten,58 H. Schoorlemmer,47 J. Schovancova,35 P. Schovánek,35 F. Schroeder,16 S. Schulte,60 F. Schüssler,16 D. Schuster,91 S. J. Sciutto,20 M. Scuderi,42 A. Segreto,12 D. Semikoz,5 M. Settimo,33 A. Shadkam,69 R. C. Shellard,23,62 I. Sidelnik,45 B. B. Siffert,56 G. Sigl,76 A. Śmiałkowski,68 R. Šmı́da,16,35 G. R. Snow,87 P. Sommers,51 J. Sorokin,22 H. Spinka,93,4 R. Squartini,46 J. Stasielak,37 M. Stephan,60 E. Strazzeri,12,49 A. Stutz,29 F. Suarez,45 T. Suomijärvi,59 A. D. Supanitsky,54 T. Šuša,11 M. S. Sutherland,25 J. Swain,84 Z. Szadkowski,28,68 A. Tamashiro,89 A. Tamburro,34 A. Tapia,45 T. Tarutina,20 O. Taşcău,28 R. Tcaciuc,19 D. Tcherniakhovski,21 D. Tegolo,42,94 N. T. Thao,63 D. Thomas,26 J. Tiffenberg,72 C. Timmermans,48,47 W. Tkaczyk,68 C. J. Todero Peixoto,77 B. Tomé,2 A. Tonachini,43 P. Travnicek,35 D. B. Tridapalli,70 G. Tristram,5 E. Trovato,42 M. Tueros,20 R. Ulrich,51,16 M. Unger,16 M. Urban,49 J. F. Valdés Galicia,54 I. Valiño,16 L. Valore,9 A. M. van den Berg,58 J. R. Vázquez,13 R. A. Vázquez,8 D. Veberič,52,66 T. Venters,17 V. Verzi,36 M. Videla,1 L. Villaseñor,50 S. Vorobiov,52 L. Voyvodic,4,* H. Wahlberg,20 P. Wahrlich,22 O. Wainberg,45 D. Warner,26 A. A. Watson,39 S. Westerhoff,30 B. J. Whelan,22 G. Wieczorek,68 L. Wiencke,91 B. Wilczyńska,37 H. Wilczyński,37 C. Williams,17 T. Winchen,60 M. G. Winnick,22 B. Wundheiler,45 T. Yamamoto,17,95 P. Younk,26 G. Yuan,69 A. Yushkov,9 E. Zas,8 D. Zavrtanik,52,66 M. Zavrtanik,66,52 I. Zaw,7 A. Zepeda,96 and M. Ziolkowski19 (Pierre Auger Collaboration) 1 National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina 2 LIP and Instituto Superior Técnico, Lisboa, Portugal 3 Istituto di Fisica dello Spazio Interplanetario (INAF), Università di Torino and Sezione INFN, Torino, Italy 4 Fermilab, Batavia, Illinois, USA 5 Laboratoire AstroParticule et Cosmologie (APC), Université Paris 7, CNRS-IN2P3, Paris, France 6 Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina 7 New York University, New York, New York, USA 8 Universidad de Santiago de Compostela, Spain 9 Università di Napoli ‘‘Federico II’’ and Sezione INFN, Napoli, Italy 10 University of Wisconsin, Milwaukee, Wisconsin, USA 11 Rudjer Bošković Institute, 10000 Zagreb, Croatia 12 Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy 13 Universidad Complutense de Madrid, Madrid, Spain 14 University of California, Los Angeles, California, USA 15 Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris 7, CNRS-IN2P3, Paris, France 16 Karlsruhe Institute of Technology—Campus North—Institut für Kernphysik, Karlsruhe, Germany 17 University of Chicago, Enrico Fermi Institute, Chicago, Illinois, USA 18 Pierre Auger Southern Observatory and Comisión Nacional de Energı́a Atómica, Malargüe, Argentina 19 Universität Siegen, Siegen, Germany 20 IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 21 Karlsruhe Institute of Technology—Campus North—Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany 22 University of Adelaide, Adelaide, S.A., Australia 23 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil 24 Universidade Estadual do Sudoeste da Bahia, Vitoria da Conquista, BA, Brazil 25 Ohio State University, Columbus, Ohio, USA 26 Colorado State University, Fort Collins, Colorado, USA 27 University of New Mexico, Albuquerque, New Mexico, USA 28 Bergische Universität Wuppertal, Wuppertal, Germany 29 Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph Fourier, INPG, CNRS-IN2P3, Grenoble, France 30 University of Wisconsin, Madison, Wisconsin, USA 31 Max-Planck-Institut für Radioastronomie, Bonn, Germany 32 Universidad de Alcalá, Alcalá de Henares (Madrid), Spain 33 Dipartimento di Fisica dell’Università del Salento and Sezione INFN, Lecce, Italy 34 Karlsruhe Institute of Technology—Campus South—Institut für Experimentelle Kernphysik (IEKP), Karlsruhe, Germany 35 Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic 36 Università di Roma II ‘‘Tor Vergata’’ and Sezione INFN, Roma, Italy 37 Institute of Nuclear Physics PAN, Krakow, Poland 38 Colorado State University, Pueblo, Colorado, USA 39 School of Physics and Astronomy, University of Leeds, United Kingdom 40 Universidad de Granada & C.A.F.P.E., Granada, Spain 091101-2 PRL 104, 091101 (2010) PHYSICAL REVIEW LETTERS week ending 5 MARCH 2010 41 Case Western Reserve University, Cleveland, Ohio, USA Università di Catania and Sezione INFN, Catania, Italy 43 Università di Torino and Sezione INFN, Torino, Italy 44 Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil 45 Centro Atómico Constituyentes (Comisión Nacional de Energı́a Atómica/CONICET/UTN-FRBA), Buenos Aires, Argentina 46 Pierre Auger Southern Observatory, Malargüe, Argentina 47 IMAPP, Radboud University, Nijmegen, Netherlands 48 NIKHEF, Amsterdam, Netherlands 49 Laboratoire de l’Accélérateur Linéaire (LAL), Université Paris 11, CNRS-IN2P3, Orsay, France 50 Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico 51 Pennsylvania State University, University Park, Pennsylvania, USA 52 Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia 53 SUBATECH, CNRS-IN2P3, Nantes, France 54 Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico 55 Università di Milano and Sezione INFN, Milan, Italy 56 Universidade Federal do Rio de Janeiro, Instituto de Fı́sica, Rio de Janeiro, RJ, Brazil 57 Universidade de São Paulo, Instituto de Fı́sica, São Carlos, SP, Brazil 58 Kernfysisch Versneller Instituut, University of Groningen, Groningen, Netherlands 59 Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris 11, CNRS-IN2P3, Orsay, France 60 RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany 61 Michigan Technological University, Houghton, Michigan, USA 62 Pontifı́cia Universidade Católica, Rio de Janeiro, RJ, Brazil 63 Institute for Nuclear Science and Technology (INST), Hanoi, Vietnam 64 University of Hawaii, Honolulu, Hawaii, USA 65 ASTRON, Dwingeloo, Netherlands 66 J. Stefan Institute, Ljubljana, Slovenia 67 Dipartimento di Fisica dell’Università and INFN, Genova, Italy 68 University of Łódź, Łódź, Poland 69 Louisiana State University, Baton Rouge, Louisiana, USA 70 Universidade de São Paulo, Instituto de Fı́sica, São Paulo, SP, Brazil 71 INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy 72 Departamento de Fı́sica, FCEyN, Universidad de Buenos Aires y CONICET, Argentina 73 Universidade Estadual de Feira de Santana, Brazil 74 Palacký University, Olomouc, Czech Republic 75 Università dell’Aquila and INFN, L’Aquila, Italy 76 Universität Hamburg, Hamburg, Germany 77 Universidade Federal do ABC, Santo André, SP, Brazil 78 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico 79 Dipartimento di Ingegneria dell’Innovazione dell’Università del Salento and Sezione INFN, Lecce, Italy 80 Southern University, Baton Rouge, Louisiana, USA 81 Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic 82 Centro de Investigaciones en Láseres y Aplicaciones, CITEFA and CONICET, Argentina 83 Instituto de Fı́sica Corpuscular, CSIC-Universitat de València, Valencia, Spain 84 Northeastern University, Boston, Massachusetts, USA 85 Caltech, Pasadena, California, USA 86 Universidade Federal da Bahia, Salvador, BA, Brazil 87 University of Nebraska, Lincoln, Nebraska, USA 88 Gran Sasso Center for Astroparticle Physics, Italy 89 Instituto de Astronomı́a y Fı́sica del Espacio (CONICET), Buenos Aires, Argentina 90 Instituto Nacional de Astrofisica, Optica y Electronica, Puebla, Mexico 91 Colorado School of Mines, Golden, Colorado, USA 92 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdom 93 Argonne National Laboratory, Argonne, Illinois, USA 94 Università di Palermo and Sezione INFN, Catania, Italy 95 Konan University, Kobe, Japan 96 Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), México, D.F., Mexico (Received 7 December 2009; published 1 March 2010) 42 We describe the measurement of the depth of maximum, Xmax , of the longitudinal development of air showers induced by cosmic rays. Almost 4000 events above 1018 eV observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are 091101-3 PRL 104, 091101 (2010) PHYSICAL REVIEW LETTERS week ending 5 MARCH 2010 selected for the analysis. The average shower maximum was found to evolve with energy at a rate of 2 18:240:05 eV, and ð24  3Þ g=cm2 =decade above this energy. The ð106þ35
21 Þ g=cm =decade below 10 measured shower-to-shower fluctuations decrease from about 55 to 26 g=cm2 . The interpretation of these results in terms of the cosmic ray mass composition is briefly discussed. DOI: 10.1103/PhysRevLett.104.091101 PACS numbers: 96.50.sd, 13.85.Tp, 96.50.sb, 98.70.Sa Introduction.—The energy dependence of the mass composition of cosmic rays is, along with the flux and arrival direction distribution, an important parameter for the understanding of the sources and propagation of cosmic rays at very high energy. There are several models that describe the observed flux of cosmic rays very well, but each of these models has different assumptions about the cosmic ray sources and correspondingly predicts a different mass composition at Earth. For example, the hardening of the cosmic ray energy spectrum at energies between 1018 and 1019 eV, known as the ‘‘ankle’’, is presumed to be either a signature of the transition from galactic to extragalactic cosmic rays or a distortion of a proton-dominated extragalactic spectrum due to energy losses [1]. Moreover, composition information may eventually help to decide whether the flux suppression observed above 4  1019 eV [2] is due mainly to the interaction of cosmic rays with the microwave background or a signature of the maximum injection energy of the sources [3]. Because of the low flux at these energies, the composition of cosmic rays cannot be measured directly, but has to be inferred from observations of extensive air showers. The atmospheric depth, Xmax , at which the longitudinal development of a shower reaches its maximum in terms of the number of secondary particles is correlated with the mass of the incident cosmic ray particle. With the generalization of Heitler’s model of electron-photon cascades to hadroninduced showers and the superposition assumption for nuclear primaries of mass A, the average depth of the shower maximum, hXmax i, at a given energy E is expected to follow [4] hXmax i ¼
ðlnE
hlnAiÞ þ ; (1) where hlnAi is the average of the logarithm of the primary masses. The coefficients
and  depend on the nature of hadronic interactions, most notably on the multiplicity, elasticity and cross section in ultrahigh energy collisions of hadrons with air, see, e.g., [5]. Although Eq. (1) is based on a simplified description of air showers, it gives a good description of air shower simulations with energyindependent parameters
and  in the energy range considered here, see [6]. Only physics processes not accounted for in currently available interaction models could lead to a significant energy dependence of these parameters. The change of hXmax i per decade of energy is called elongation rate [7], D10 ¼
 dhXmax i dhlnAi 
1
lnð10Þ; d lgE d lnE (2) and it is sensitive to changes in composition with energy. A complementary composition-dependent observable is the magnitude of the shower-to-shower fluctuations of the depth of maximum, rmsðXmax Þ, which is expected to decrease with the of primary nucleons A (though not pffiffiffinumber ffi as fast as 1= A [8]) and to increase with the interaction length of the primary particle. At ultrahigh energies, the shower maximum can be observed directly with fluorescence detectors. Previously published Xmax measurements [9,10] focused mainly on hXmax i as a function of energy and had only limited statistics above 1019 eV. Here we present a measurement of both hXmax i and rmsðXmax Þ using high quality and high statistics data collected with the southern site of the Pierre Auger Observatory [11]. The observatory is located in the province of Mendoza, Argentina and consists of two detectors. The surface detector (SD) array comprises 1600 waterCherenkov detectors arranged on a triangular grid with 1500 m spacing that cover an area of over 3000 km2 . The water-Cherenkov detectors are sensitive to the air shower components at ground level. The fluorescence detector (FD) consists of 24 optical telescopes overlooking the array, which can observe the longitudinal shower development by detecting the fluorescence and Cherenkov light produced by charged particles along the shower trajectory in the atmosphere. Data analysis.—This work is based on air shower data recorded between December 2004 and March 2009. Only events detected in the hybrid mode [12] are considered; i.e., the shower development must have been measured by the FD, and at least one coincident SD station is required to provide a ground-level time. Using the time constraint from the SD, the shower geometry can be determined with an angular uncertainty of 0.6 [13]. The longitudinal profile of the energy deposit is reconstructed [14] from the light recorded by the FD using the fluorescence and Cherenkov yields and lateral distributions from [15]. With the help of data from atmospheric monitoring devices [16] the light collected by the telescopes is corrected for the attenuation between the shower and the detector and the longitudinal shower profile is reconstructed as a function of atmospheric depth. Xmax is determined by fitting the reconstructed longitudinal profile with a Gaisser-Hillas function [17]. 091101-4 week ending 5 MARCH 2010 PHYSICAL REVIEW LETTERS Xmax resolution [g/cm2 ] data RMS = 20± 2 (stat.) g/cm2 25 MC RMS = 19+2 (syst.) g/cm2 −1 20 entries An unbiased set of high quality events is selected with the statistical uncertainty of the reconstructed Xmax being comparable to the size of the fluctuations expected for nuclei as heavy as iron (20 g=cm2 ) and small systematic uncertainties as explained in the following. The impact of varying atmospheric conditions on the Xmax measurement is minimized by rejecting time periods with cloud coverage and by requiring reliable measurements of the vertical optical depth of aerosols. Profiles that are distorted by residual cloud contamination are rejected by a loose cut on the quality of the profile fit (2 =Ndf < 2:5). We take into account events only with energies above 1018 eV where the probability for at least one triggered SD station is 100%, irrespective of the mass of the primary particle [18]. The geometrical reconstruction of showers with a large apparent angular speed of the image in the telescope is susceptible to uncertainties in the time synchronization between FD and SD. Therefore, events with a light emission angle towards the FD that is smaller than 20 are rejected. This cut also removes events with a large fraction of Cherenkov light. The energy and shower maximum can be reliably measured only if Xmax is in the field of view (FOV) of the telescopes (covering 1.5 to 30 in elevation). Events for which only the rising or falling edge of the profile is detected are not used. Moreover, we calculate the expected statistical uncertainty of the reconstruction of Xmax for each event, based on the shower geometry and atmospheric conditions, and require it to be better than 40 g=cm2 . The latter two selection criteria may cause a selection bias due to a systematic undersampling of the tails of the true Xmax distribution, since showers developing very deep or shallow in the atmosphere might be rejected from the data sample. To avoid such a bias in the measured hXmax i and rmsðXmax Þ we apply fiducial volume cuts based on the shower geometry that ensure that the viewable Xmax range for each shower is large enough to accommodate the full Xmax distribution [19]. After all cuts, 3754 events are selected for the Xmax analysis. The Xmax resolution as a function of energy for these events is estimated using a detailed simulation of the FD and the atmosphere. As shown in the inset of Fig. 1, the resolution is at the 20 g=cm2 level above a few EeV. The difference between the reconstructed Xmax values in events that had a sufficiently high energy to be detected independently by two or more FD stations is used to cross-check these findings. As can be seen in Fig. 1, the simulations reproduce the data well. Results and discussion.—The measured hXmax i and rmsðXmax Þ values are shown in Figs. 2 and 3. We use bins of
lgE ¼ 0:1 below 10 EeV and
lgE ¼ 0:2 above that energy. The last bin starts at 1019:4 eV, integrating up to the highest energy event (E ¼ ð59  8Þ EeV). The systematic uncertainty of the FD energy scale is 22% [18]. Uncertainties of the calibration, atmospheric conditions, 15 35 30 25 20 15 10 MC ± sys. 5 0 18 10 19 10 20 10 E [eV] 10 5 0 −80 −60 −40 −20 0 20 40 60 80 ∆Xmax/ 2 [g/cm2] FIG. 1. Difference between Xmax measured in showers simultaneously at two FD stations (hlgðE=eVÞi ¼ 19:1). The Xmax resolution is displayed as a function of energy in the inset. reconstruction and event selection give rise to a systematic uncertainty of 13 g=cm2 for hXmax i and 6 g=cm2 for the rms. The results were found to be independent of zenith angle, time periods and FD stations within the experimental uncertainties. A fit of the measured hXmax i values with a constant elongation rate does not describe our data (2 =Ndf ¼ 34:9=11), but as can be seen in Fig. 2, using two slopes yields a satisfactory fit (2 =Ndf ¼ 9:7=9) with an elonga2 18:240:05 eV tion rate of ð106þ35
21 Þ g=cm =decade below 10 2 and ð24  3Þ g=cm =decade above this energy. If the properties of hadronic interactions do not change significantly over less than 2 orders of magnitude in primary energy (< factor 10 in center of mass energy), this change of 2
D10 ¼ ð82þ35
21 Þ g=cm =decade would imply a change in the energy dependence of the composition around the Auger 09 800 HiRes ApJ05 780 <Xmax> [g/cm2] PRL 104, 091101 (2010) 760 740 34 720 372 552 452 700 278 196 147 131 138 96 broken line fit ± sys. 602 685 680 18 10 71 19 10 E [eV] FIG. 2. hXmax i as a function of energy. Lines denote a fit with a broken line in lgE. The systematic uncertainties of hXmax i are indicated by a dashed line. The number of events in each energy bin is displayed below the data points. HiRes data [10] are shown for comparison. 091101-5 QGSJET01 QGSJETII Sibyll2.1 EPOSv1.99 <X max> [g/cm2] 850 on prot 70 800 750 iron 700 proton 60 50 40 30 20 iron 10 650 18 10 0 19 10 18 10 E [eV] FIG. 3. week ending 5 MARCH 2010 PHYSICAL REVIEW LETTERS RMS(Xmax) [g/cm2] PRL 104, 091101 (2010) 19 10 E [eV] hXmax i and rmsðXmax Þ compared with air shower simulations [20] using different hadronic interaction models [21]. ankle, supporting the hypothesis of a transition from galactic to extragalactic cosmic rays in this region. The hXmax i result of this analysis is compared to the HiRes data [10] in Fig. 2. Both data sets agree well within the quoted systematic uncertainties. The 2 =Ndf of the HiRes data with respect to the broken-line fit described above is 20:5=14. This value reduces to 16:8=14 if a relative energy shift of 15% is applied, such as suggested by a comparison of the Auger and HiRes energy spectra [2]. The shower-to-shower fluctuations, rmsðXmax Þ, are obtained by subtracting the detector resolution in quadrature from the width of the observed Xmax distributions resulting in a correction of  6 g=cm2 . As can be seen in the right panel of Fig. 3, we observe a decrease in the fluctuations with energy from about 55 to 26 g=cm2 as the energy increases. Assuming again that the hadronic interaction properties do not change much within the observed energy range, these decreasing fluctuations are an independent signature of an increasing average mass of the primary particles. For the interpretation of the absolute values of hXmax i and rmsðXmax Þ a comparison to air shower simulations is needed. As can be seen in Fig. 3, there are considerable differences between the results of calculations using different hadronic interaction models. These differences are not necessarily exhaustive, since the hadronic interaction models do not cover the full range of possible extrapolations of low energy accelerator data. If, however, these models provide a realistic description of hadronic interactions at ultrahigh energies, the comparison of the data and simulations leads to the same conclusions as above, namely, a gradual increase of the average mass of cosmic rays with energy up to 59 EeV. The successful installation and commissioning of the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the technical and administrative staff in Malargüe. We are very grateful to the following agencies and organizations for financial support: Comisión Nacional de Energı́a Atómica, Fundación Antorchas, Gobierno De La Provincia de Mendoza, Municipalidad de Malargüe, NDM Holdings, and Valle Las Leñas, in gratitude for their continuing cooperation over land access, Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro (FAPERJ), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Ministério de Ciência e Tecnologia (MCT), Brazil; AVCR AV0Z10100502 and AV0Z10100522, GAAV KJB300100801 and KJB100100904, MSMT-CR LA08016, LC527, 1M06002, and MSM0021620859, Czech Republic; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientifique (CNRS), Conseil Régional Ile-de-France, Département Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS), Département Sciences de l’Univers (SDU-INSU/CNRS), France; Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Finanzministerium Baden-Württemberg, Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ministerium für Wissenschaft und Forschung, Nordrhein-Westfalen, Ministerium für Wissenschaft, Forschung und Kunst, Baden-Württemberg, Germany; Istituto Nazionale di Fisica Nucleare (INFN), Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR), Italy; Consejo Nacional de Ciencia y Tecnologı́a (CONACYT), Mexico; Ministerie van Onderwijs, Cultuur en Wetenschap, Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Fundamenteel Onderzoek der Materie (FOM), Netherlands; Ministry of Science and Higher Education, Grant No. 1 P03 D 014 30, No. N202 090 31/0623, and No. PAP/218/2006, Poland; Fundação para a Ciência e a Tecnologia, Portugal; Ministry for Higher Education, Science, and Technology, Slovenian Research Agency, Slovenia; Comunidad de Madrid, Consejerı́a de Educación de la Comunidad de Castilla La 091101-6 PRL 104, 091101 (2010) PHYSICAL REVIEW LETTERS Mancha, FEDER funds, Ministerio de Ciencia e Innovación, Xunta de Galicia, Spain; Science and Technology Facilities Council, United Kingdom; Department of Energy, Contract No. DE-AC0207CH11359, No. DE-FR02-04ER41300, National Science Foundation, Grant No. 0450696, The Grainger Foundation USA; ALFA-EC/HELEN, European Union 6th Framework Program, Grant No. MEIF-CT-2005025057, European Union 7th Framework Program, Grant No. PIEF-GA-2008-220240, and UNESCO. *Deceased. [1] A. M. Hillas, Phys. Lett. 24, 677 (to be published); V. S. Berezinsky and S. I. Grigor’eva, Astron. Astrophys. 199, 1 (1988); D. Allard, E. Parizot, and A. V. Olinto, Astropart. Phys. 27, 61 (2007); R. Aloisio, V. Berezinsky, P. Blasi, and S. Ostapchenko, Phys. Rev. D 77, 025007 (2008). [2] R. Abbasi et al. (HiRes Collaboration), Phys. Rev. Lett. 100, 101101 (2008); J. Abraham et al. (Pierre Auger Collaboration), Phys. Rev. Lett. 101, 061101 (2008). [3] D. Allard et al., J. Cosmol. Astropart. Phys. 10 (2008) 033. [4] W. Heitler, The Quantum Theory of Radiation (Oxford University Press, New York, 1954); J. Matthews, Astropart. Phys. 22, 387 (2005). [5] T. Wibig, Phys. Rev. D 79, 094008 (2009); R. Ulrich et al., arXiv:0906.0418 [Proc. 31st ICRC (to be published)]. [6] T. Pierog, R. Engel, and D. Heck, Czech. J. Phys. 56, A161 (2006); J. Bluemer, R. Engel, and J. R. Hoerandel, Prog. Part. Nucl. Phys. 63, 293 (2009). [7] J. Linsley, Proceedings of the 15th ICRC, Vol. 12, p. 89 (Hungarian Academy of Sciences, Budapest, 1977); T. K. Gaisser et al., Proceedings of the 16th ICRC, Vol. 9, p. 275 (Institute for Cosmic Ray Research, Tokyo, 1979); J. Linsley and A. A. Watson, Phys. Rev. Lett. 46, 459 (1981). [8] J. Engel et al., Phys. Rev. D 46, 5013 (1992). week ending 5 MARCH 2010 [9] D. J. Bird et al. (Fly’s Eye Collaboration), Phys. Rev. Lett. 71, 3401 (1993). [10] R. U. Abbasi et al. (HiRes Collaboration), Astrophys. J. 622, 910 (2005). [11] J. Abraham et al. (Pierre Auger Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 523, 50 (2004); J. Abraham et al. (Pierre Auger Collaboration), arXiv:0907.4282 [Nucl. Instrum. Meth. (to be published)]; I. Allekotte et al. (Pierre Auger Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 586, 409 (2008). [12] P. Sommers, Astropart. Phys. 3, 349 (1995); B. R. Dawson et al., Astropart. Phys. 5, 239 (1996). [13] C. Bonifazi et al. (Pierre Auger Collaboration), Nucl. Phys. B, Proc. Suppl. 190, 20 (2009). [14] M. Unger et al., Nucl. Instrum. Methods Phys. Res., Sect. A 588, 433 (2008). [15] M. D. Roberts, J. Phys. G 31, 1291 (2005); D. Gora et al., Astropart. Phys. 24, 484 (2006); F. Nerling et al., Astropart. Phys. 24, 421 (2006); B. R. Dawson, M. Giller, and G. Wieczorek, Proceedings of the 30th ICRC (2007); B. Keilhauer et al., Nucl. Instrum. Methods Phys. Res., Sect. A 597, 99 (2008). [16] J. Abraham et al. (Pierre Auger Collaboration), arXiv:0906.2358 [Proc. 31st ICRC (to be published)]. [17] T. K. Gaisser and A. M. Hillas, Proceedings of the 15th ICRC, Vol. 8, p. 353 (1977). [18] J. Abraham et al. (Pierre Auger Collaboration), arXiv:0906.2189 [Proc. 31st ICRC (to be published)]. [19] M. Unger (Pierre Auger Coll.), Nucl. Phys. B, Proc. Suppl. 190, 240 (2009); J. A. Bellido (Pierre Auger Coll.), arXiv:0901.3389 [Proc. XXth Rencontres de Blois (to be published)]. [20] T. Bergmann et al., Astropart. Phys. 26, 420 (2007). [21] N. N. Kalmykov and S. S. Ostapchenko, Phys. At. Nucl. 56, 346 (1993); S. S. Ostapchenko, Nucl. Phys. B, Proc. Suppl. 151, 143 (2006); T. Pierog and K. Werner, Phys. Rev. Lett. 101, 171101 (2008); E. J. Ahn et al., Phys. Rev. D 80, 094003 (2009). 091101-7 PUBLISHED VERSION