Azimuthal asymmetry in the risetime of the surface detector signals of the Pierre Auger Observatory
Pierre Auger Collaboration, A. Aab, P. Abreu, M. Aglietta, E.J. Ahn, I. Al Samarai, I.F.M. Albuquerque, I. Allekotte, P. Allison, A. Almela, J. Alvarez Castillo, J. Alvarez-Muñiz, M. Ambrosio, G.A. Anastasi, L. Anchordoqui, B. Andrada, S. Andringa, C. Aramo, F. Arqueros, N. Arsene, H. Asorey, P. Assis, J. Aublin, G. Avila, N. Awal, A.M. Badescu, C. Baus, J.J. Beatty, K.H. Becker, J.A. Bellido, C. Berat, M.E. Bertaina, X. Bertou, P.L. Biermann, P. Billoir, J. Biteau, S.G. Blaess, A. Blanco, J. Blazek, C. Bleve, H. Blümer, M. Boháčová, D. Boncioli, C. Bonifazi, N. Borodai, A.M. Botti, J. Brack, I. Brancus, T. Bretz, A. Bridgeman, F.L. Briechle, P. Buchholz, A. Bueno, S. Buitink, M. Buscemi, K.S. Caballero-Mora, B. Caccianiga, L. Caccianiga, A. Cancio, F. Canfora, L. Caramete, R. Caruso, A. Castellina, G. Cataldi, L. Cazon, R. Cester, A.G. Chavez, A. Chiavassa, J.A. Chinellato, J. Chudoba, R.W. Clay, R. Colalillo, A. Coleman, L. Collica, M.R. Coluccia, R. Conceição, F. Contreras, M.J. Cooper, S. Coutu, C.E. Covault, J. Cronin, R. Dallier, S. D'Amico, B. Daniel, S. Dasso, K. Daumiller, B.R. Dawson, R.M. de Almeida, S.J. de Jong, G. De Mauro, J.R.T. de Mello Neto, I. De Mitri, J. de Oliveira, V. de Souza, J. Debatin, L. del Peral, O. Deligny, N. Dhital, C. Di Giulio, A. Di Matteo, et al. (339 additional authors not shown)
PPublished in Phys. Rev. D as DOI:http://dx.doi.org/10.1103/PhysRevD.93.072006
Azimuthal asymmetry in the risetime of the surface detector signals of the Pierre AugerObservatory
A. Aab, P. Abreu, M. Aglietta,
3, 4
E.J. Ahn, I. Al Samarai, I.F.M. Albuquerque, I. Allekotte, P. Allison, A. Almela,
10, 11
J. Alvarez Castillo, J. Alvarez-Mu˜niz, R. Alves Batista, M. Ambrosio, L. Anchordoqui, B. Andrada, S. Andringa, C. Aramo, F. Arqueros, N. Arsene, H. Asorey,
8, 19
P. Assis, J. Aublin, G. Avila,
20, 21
N. Awal, A.M. Badescu, C. Baus, J.J. Beatty, K.H. Becker, J.A. Bellido, C. Berat, M.E. Bertaina,
28, 4
X. Bertou, P.L. Biermann, P. Billoir, S.G. Blaess, A. Blanco, J. Blazek, C. Bleve,
31, 32
H. Bl¨umer,
24, 33
M. Boh´aˇcov´a, D. Boncioli,
34, 35
C. Bonifazi, N. Borodai, A.M. Botti,
10, 33
J. Brack, I. Brancus, T. Bretz, A. Bridgeman, F.L. Briechle, P. Buchholz, A. Bueno, S. Buitink, M. Buscemi,
43, 44
K.S. Caballero-Mora, B. Caccianiga, L. Caccianiga, A. Cancio,
11, 10
M. Candusso, L. Caramete, R. Caruso,
43, 44
A. Castellina,
3, 4
G. Cataldi, L. Cazon, R. Cester,
28, 4
A.G. Chavez, A. Chiavassa,
28, 4
J.A. Chinellato, J.C. Chirinos Diaz, J. Chudoba, R.W. Clay, R. Colalillo,
52, 15
A. Coleman, L. Collica, M.R. Coluccia,
31, 32
R. Conceic¸ ˜ao, F. Contreras,
20, 21
M.J. Cooper, S. Coutu, C.E. Covault, J. Cronin, R. Dallier,
56, 57
S. D’Amico,
58, 32
B. Daniel, S. Dasso,
59, 60
K. Daumiller, B.R. Dawson, R.M. de Almeida, S.J. de Jong,
42, 62
G. De Mauro, J.R.T. de Mello Neto, I. De Mitri,
31, 32
J. de Oliveira, V. de Souza, J. Debatin, O. Deligny, N. Dhital, C. Di Giulio,
65, 47
A. Di Matteo,
66, 67
M.L. D´ıaz Castro, F. Diogo, C. Dobrigkeit, W. Docters, J.C. D’Olivo, A. Dorofeev, R.C. dos Anjos, M.T. Dova, A. Dundovic, J. Ebr, R. Engel, M. Erdmann, M. Erfani, C.O. Escobar,
5, 50
J. Espadanal, A. Etchegoyen,
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72, 73
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F. Gallo, B. Garc´ıa, D. Garcia-Pinto, F. Gate, H. Gemmeke, A. Gherghel-Lascu, P.L. Ghia, U. Giaccari, M. Giammarchi, M. Giller, D. Głas, C. Glaser, H. Glass, G. Golup, M. G´omez Berisso, P.F. G´omezVitale,
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N. Gonz´alez,
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C. Jarne, J.A. Johnsen, M. Josebachuili, A. K¨a¨ap¨a, O. Kambeitz, K.H. Kampert, P. Kasper, I. Katkov, B. Keilhauer, E. Kemp, R.M. Kieckhafer, H.O. Klages, M. Kleifges, J. Kleinfeller, R. Krause, N. Krohm, D. Kuempel, G. Kukec Mezek, N. Kunka, A. Kuotb Awad, D. LaHurd, L. Latronico, M. Lauscher, P. Lautridou, P. Lebrun, M.A. Leigui de Oliveira, A. Letessier-Selvon, I. Lhenry-Yvon, K. Link, L. Lopes, R. L´opez, A. L´opez Casado, A. Lucero,
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D. Martello,
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D. Maurizio, E. Mayotte, P.O. Mazur, C. Medina, G. Medina-Tanco, V.B.B. Mello, D. Melo, A. Menshikov, S. Messina, M.I. Micheletti, L. Middendorf, I.A. Minaya, L. Miramonti,
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B. Mitrica, L. Molina-Bueno, S. Mollerach, F. Montanet, C. Morello,
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M. Mostaf´a, C.A. Moura, G. M¨uller, M.A. Muller,
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I. Naranjo, S. Navas, P. Necesal, L. Nellen, A. Nelles,
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J. Neuser, P.H. Nguyen, M. Niculescu-Oglinzanu, M. Niechciol, L. Niemietz, T. Niggemann, D. Nitz, D. Nosek, V. Novotny, H. Noˇzka, L.A. N´u˜nez, L. Ochilo, F. Oikonomou, A. Olinto, D. Pakk Selmi-Dei, M. Palatka, J. Pallotta, P. Papenbreer, G. Parente, A. Parra, T. Paul,
92, 16
M. Pech, J. Pe¸kala, R. Pelayo, J. Pe˜na-Rodriguez, I.M. Pepe, L. A. S. Pereira, L. Perrone,
31, 32
E. Petermann, C. Peters, S. Petrera,
66, 67
J. Phuntsok, R. Piegaia, T. Pierog, P. Pieroni, M. Pimenta, V. Pirronello,
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M. Platino, M. Plum, C. Porowski, R.R. Prado, P. Privitera, M. Prouza, E.J. Quel, S. Querchfeld, S. Quinn, J. Rautenberg, O. Ravel, D. Ravignani, D. Reinert, B. Revenu, J. Ridky, M. Risse, P. Ristori, V. Rizi,
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W. Rodrigues de Carvalho, J. Rodriguez Rojo, D. Rogozin, J. Rosado, M. Roth, E. Roulet, A.C. Rovero, S.J. Saffi, A. Saftoiu, H. Salazar, A. Saleh, F. Salesa Greus, G. Salina, J.D. Sanabria Gomez, F. S´anchez, P. Sanchez-Lucas, E.M. Santos, E. Santos, F. Sarazin, B. Sarkar, R. Sarmento, C. Sarmiento-Cano, R. Sato, C. Scarso, M. Schauer, V. Scherini,
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H. Schieler, D. Schmidt,
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O. Scholten,
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H. Schoorlemmer, P. Schov´anek, F.G. Schr¨oder, A. Schulz, J. Schulz, J. Schumacher, S.J. Sciutto, A. Segreto,
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M. Settimo, A. Shadkam, R.C. Shellard, G. Sigl, O. Sima, A. ´Smiałkowski, R. ˇSm´ıda, G.R. Snow, P. Sommers, S. Sonntag, J. Sorokin, R. Squartini, D. Stanca, S. Staniˇc, J. Stapleton, J. Stasielak, F. Strafella,
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A. Stutz, F. Suarez,
10, 11
M. Suarez Dur´an, T. Sudholz, T. Suomij¨arvi, A.D. Supanitsky, M.S. Sutherland, J. Swain, Z. Szadkowski, O.A. Taborda, A. Tapia, A. Tepe, V.M. Theodoro, C. Timmermans,
62, 42
C.J. Todero Peixoto, L. Tomankova, B. Tom´e, A. Tonachini,
28, 4
G. Torralba Elipe, D. TorresMachado, P. Travnicek, M. Trini, R. Ulrich, M. Unger,
22, 33
M. Urban, J.F. Vald´es Galicia, I. Vali˜no, L. Valore,
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G. van Aar, P. van Bodegom, A.M. van den Berg, A. van Vliet, E. Varela, B. Vargas C´ardenas, G. Varner, a r X i v : . [ a s t r o - ph . H E ] A p r R. Vasquez, J.R. V´azquez, R.A. V´azquez, D. Veberiˇc, V. Verzi, J. Vicha, M. Videla, L. Villase˜nor, S. Vorobiov, H. Wahlberg, O. Wainberg,
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D. Walz, A.A. Watson, M. Weber, A. Weindl, L. Wiencke, H. Wilczy´nski, T. Winchen, D. Wittkowski, B. Wundheiler, S. Wykes, L. Yang, T. Yapici, D. Yelos,
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A. Yushkov, E. Zas, D. Zavrtanik,
73, 72
M. Zavrtanik,
72, 73
A. Zepeda, B. Zimmermann, M. Ziolkowski, Z. Zong, and F. Zuccarello
43, 44 (The Pierre Auger Collaboration) ∗ Universit¨at Siegen, Fachbereich 7 Physik – Experimentelle Teilchenphysik, Germany Laborat´orio de Instrumentac¸ ˜ao e F´ısica Experimental de Part´ıculas – LIPand Instituto Superior T´ecnico – IST, Universidade de Lisboa – UL, Portugal Osservatorio Astrofisico di Torino (INAF), Torino, Italy INFN, Sezione di Torino, Italy Fermi National Accelerator Laboratory, USA Laboratoire de Physique Nucl´eaire et de Hautes Energies (LPNHE), Universit´es Paris 6 et Paris 7, CNRS-IN2P3, France Universidade de S˜ao Paulo, Inst. de F´ısica, S˜ao Paulo, Brazil Centro At´omico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), Argentina Ohio State University, USA Instituto de Tecnolog´ıas en Detecci´on y Astropart´ıculas (CNEA, CONICET, UNSAM),Centro At´omico Constituyentes, Comisi´on Nacional de Energ´ıa At´omica, Argentina Universidad Tecnol´ogica Nacional – Facultad Regional Buenos Aires, Argentina Universidad Nacional Aut´onoma de M´exico, M´exico Universidad de Santiago de Compostela, Spain Universit¨at Hamburg, II. Institut f¨ur Theoretische Physik, Germany INFN, Sezione di Napoli, Italy Department of Physics and Astronomy, Lehman College, City University of New York, USA Universidad Complutense de Madrid, Spain University of Bucharest, Physics Department, Romania Universidad Industrial de Santander, Colombia Observatorio Pierre Auger, Argentina Observatorio Pierre Auger and Comisi´on Nacional de Energ´ıa At´omica, Argentina New York University, USA University Politehnica of Bucharest, Romania Karlsruhe Institute of Technology, Institut f¨ur Experimentelle Kernphysik (IEKP), Germany Bergische Universit¨at Wuppertal, Fachbereich C – Physik, Germany University of Adelaide, Australia Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit´e Grenoble-Alpes, CNRS/IN2P3, France Universit`a Torino, Dipartimento di Fisica, Italy Max-Planck-Institut f¨ur Radioastronomie, Bonn, Germany Institute of Physics (FZU) of the Academy of Sciences of the Czech Republic, Czech Republic Universit`a del Salento, Dipartimento di Matematica e Fisica “E. De Giorgi”, Italy INFN, Sezione di Lecce, Italy Karlsruhe Institute of Technology, Institut f¨ur Kernphysik (IKP), Germany INFN Laboratori del Gran Sasso, Italy also at Deutsches Elektronen-Synchrotron (DESY), Zeuthen, Germany Universidade Federal do Rio de Janeiro (UFRJ), Instituto de F´ısica, Brazil Institute of Nuclear Physics PAN, Poland Colorado State University, USA “Horia Hulubei” National Institute for Physics and Nuclear Engineering, Romania RWTH Aachen University, III. Physikalisches Institut A, Germany Universidad de Granada and C.A.F.P.E., Spain Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud Universiteit, Nijmegen, Netherlands Universit`a di Catania, Dipartimento di Fisica e Astronomia, Italy INFN, Sezione di Catania, Italy Universidad Aut´onoma de Chiapas, M´exico INFN, Sezione di Milano, Italy INFN, Sezione di Roma “Tor Vergata”, Italy Institute of Space Science, Romania Universidad Michoacana de San Nicol´as de Hidalgo, M´exico Universidade Estadual de Campinas (UNICAMP), Brazil Michigan Technological University, USA Universit`a di Napoli “Federico II”, Dipartimento di Fisica, Italy Pennsylvania State University, USA Case Western Reserve University, USA University of Chicago, USA SUBATECH, ´Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes, France Station de Radioastronomie de Nanc¸ay, France Universit`a del Salento, Dipartimento di Ingegneria, Italy Instituto de Astronom´ıa y F´ısica del Espacio (IAFE, CONICET-UBA), Argentina Departamento de F´ısica, FCEyN, Universidad de Buenos Aires, Argentina Universidade Federal Fluminense, Brazil Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Netherlands Universidade de S˜ao Paulo, Inst. de F´ısica de S˜ao Carlos, S˜ao Carlos, Brazil Institut de Physique Nucl´eaire d’Orsay (IPNO), Universit´e Paris 11, CNRS-IN2P3, France Universit`a di Roma “Tor Vergata”, Dipartimento di Fisica, Italy Universit`a dell’Aquila, Dipartimento di Chimica e Fisica, Italy INFN, Sezione di L’Aquila, Italy KVI – Center for Advanced Radiation Technology, University of Groningen, Netherlands Universidade Federal do Paran´a, Setor Palotina, Brazil IFLP, Universidad Nacional de La Plata and CONICET, Argentina Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, Netherlands Experimental Particle Physics Department, J. Stefan Institute, Slovenia Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia Instituto de F´ısica de Rosario (IFIR) – CONICET/U.N.R. and Facultad de Ciencias Bioqu´ımicas y Farmac´euticas U.N.R., Argentina Instituto de Tecnolog´ıas en Detecci´on y Astropart´ıculas (CNEA, CONICET,UNSAM) and Universidad Tecnol´ogica Nacional – Facultad Regional Mendoza (CONICET/CNEA), Argentina Karlsruhe Institute of Technology, Institut f¨ur Prozessdatenverarbeitung und Elektronik (IPE), Germany University of Ł´od´z, Poland University of Hawaii, USA Universidade Estadual de Feira de Santana (UEFS), Brazil Palacky University, RCPTM, Czech Republic Colorado School of Mines, USA Universidade Federal do ABC (UFABC), Brazil Benem´erita Universidad Aut´onoma de Puebla (BUAP), M´exico Universit`a di Milano, Dipartimento di Fisica, Italy Centro de Investigaci´on y de Estudios Avanzados del IPN (CINVESTAV), M´exico Louisiana State University, USA University of New Mexico, USA Centro Brasileiro de Pesquisas Fisicas (CBPF), Brazil Universidade Federal de Pelotas, Brazil University Prague, Institute of Particle and Nuclear Physics, Czech Republic Centro de Investigaciones en L´aseres y Aplicaciones, CITEDEF and CONICET, Argentina Northeastern University, USA Unidad Profesional Interdisciplinaria en Ingenier´ıa y Tecnolog´ıas Avanzadas del Instituto Polit´ecnico Nacional (UPIITA-IPN), M´exico Universidade Federal da Bahia, Brazil University of Nebraska, USA also at Vrije Universiteit Brussels, Brussels, Belgium INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Italy Universidade de S˜ao Paulo, Escola de Engenharia de Lorena, Brazil School of Physics and Astronomy, University of Leeds, Leeds, United Kingdom
The azimuthal asymmetry in the risetime of signals in Auger surface detector stations is a source of informa-tion on shower development. The azimuthal asymmetry is due to a combination of the longitudinal evolutionof the shower and geometrical effects related to the angles of incidence of the particles into the detectors. Themagnitude of the effect depends upon the zenith angle and state of development of the shower and thus pro-vides a novel observable, (sec θ ) max , sensitive to the mass composition of cosmic rays above × eV. Bycomparing measurements with predictions from shower simulations, we find for both of our adopted models ofhadronic physics (QGSJETII-04 and EPOS-LHC) an indication that the mean cosmic-ray mass increases slowlywith energy, as has been inferred from other studies. However, the mass estimates are dependent on the showermodel and on the range of distance from the shower core selected. Thus the method has uncovered furtherdeficiencies in our understanding of shower modelling that must be resolved before the mass composition canbe inferred from (sec θ ) max . PACS numbers: 13.85.Tp, 96.50.sd, 96.50.sb, 98.70.Sa ∗ I. INTRODUCTION
A detailed understanding of the properties and origin ofcosmic rays with energies greater than 1 Joule ( . × eV)remains incomplete over 50 years since their discovery [1].An explanation for the origin of these particles must accountfor the observations of their energy spectrum, arrival direc-tion distributions and mass composition. Determination of themass composition from measurements of extensive air show-ers is by far the greatest challenge as it is necessary to makeassumptions about the hadronic physics in regions of phasespace not covered by measurements at accelerators: for exam-ple, the center-of-mass energy that will ultimately be reachedat the LHC corresponds to that reached in a collision of a pro-ton of only eV with a stationary nucleon. It follows thatin the region of interest here, from to eV, there is aserious lack of knowledge of how key parameters such as thecross-section, the multiplicity and the inelasticity in collisionsof protons and nuclei on nuclei, and of charged pions on nu-clei, depend on energy. Furthermore, at the LHC, studies arerestricted to relatively small rapidities whereas at air-showerenergies the behavior at large Feynman x is of great signifi-cance.Lack of knowledge of the hadronic processes is a less se-rious issue when deriving the energy spectrum following thesuccessful demonstration of calorimetric estimates of the en-ergies of cosmic rays using the fluorescence technique [2, 3].In determining the energy account must be taken of the “in-visible energy” carried by neutrinos and by muons taken intothe earth beyond the reach of the fluorescence detectors andthe unknowns of mass composition and hadronic physics areimportant at about the 10% level. Methods are also being de-veloped to estimate the invisible energy on an event-by-eventbasis [4]. In [2, 3] convincing evidence for a suppression ofthe spectrum flux above ∼ × eV was reported. How-ever, to interpret the shape of the spectrum in detail requiresknowledge of the mass composition at the highest energies.The fluorescence technique can be used to get informationthat relates to the mass composition. It has been used to mea-sure the average depth and spread of the distribution of pointsat which the number of particles in the shower maximizes, X max , as a function of energy. Measurements of X max basedon observations of nearly 20000 events above . × eVhave recently been reported [5]. However only 37 of theseevents have energies above . × eV, a number con-strained by the on-time of fluorescence detectors which is < . Detailed analyses of the distributions of X max innarrow energy bins, made using three models of the hadronicinteraction, Sibyll 2.1 [6], QGSJETII-04 [7] and EPOS-LHC[8], lead to the conclusion that helium and nitrogen are themost abundant elements above . × eV [9].The lack of compositional information at the highest ener-gies is also a severe problem for the interpretation of the dis-tributions of arrival directions. For example the high degree ofisotropy observed in numerous tests of the small-scale angu-lar distributions of ultra-high energy cosmic rays (UHECR)is remarkable, challenging earlier expectations that assumedonly a few cosmic-ray sources producing light primaries at the highest energies. In fact the largest departures from isotropyare observed for cosmic rays above . × eV in sky-windows of about 20 ◦ [10], while at energies above 8 EeV,there are indications of a dipole in the distribution of arrivaldirections [11].One way to increase the sample, and so test the interactionmodels, is to develop techniques using the water-Cherenkovdetectors of the surface array of the Auger Observatory [12],which operate ∼ × eV. However the variation of mass with energy,deduced when the depth of maximum of muon production( X max µ ) is compared to the predictions of the QGSJETII-04and EPOS-LHC hadronic models, does not agree with what isfound from the fluorescence detector (FD) measurements sug-gesting that the part of the hadronic development that relatesto muon creation is modelled incorrectly.In this paper a further exploration of the model-mass pa-rameter space is described using an observable from the water-Cherenkov detectors that is related to the azimuthal asymme-try found in the risetime of the signals with respect to the di-rection of the incoming air shower. The asymmetry is due toa combination of the longitudinal development of the showerand of geometrical effects and thus has the potential to givealternative insights into the matching of data to mass andhadronic models using a technique with quite different sys-tematic uncertainties to those of the MPD or FD approaches.As both the muonic and electromagnetic components con-tribute to the risetime, the technique explores the region be-tween the dominantly electromagnetic study of X max and theMPD analysis which is muon-based.The structure of the paper is as follows. In the followingsection the Auger Observatory is briefly outlined with em-phasis on aspects that are important for this paper. In sec-tion III the concept of the asymmetry of the risetime is de-scribed while in section IV details of the analysis of this asym-metry are presented. The results are shown in section V anddiscussed in section VI where they are compared with thosefrom the fluorescence detector and the MPD analyses. II. THE OBSERVATORY AND EVENTRECONSTRUCTION
The Pierre Auger Observatory is located in the Province ofMendoza, Argentina (35.1 ◦ - 35.5 ◦ S, 69.0 ◦ - 69.6 ◦ W, 1400 ma.s.l.). It is a hybrid system, a combination of a large surface-detector array (SD) and a fluorescence detector which recordscosmic-ray events above eV. The work presented in thefollowing is based on data from the SD. As data from the FDwill also be referred to, we summarize here the main charac-teristics of the two detectors as well as the principles of theevent reconstruction. More details on the detectors and on theevent reconstruction can be found in [12, 14–16].The surface detector array, covering an area of over 3000km , comprises 1600 units, which are arranged on a trian-gular grid with 1500 m spacing. It samples the electromag- FIG. 1. Schematic view of the shower geometry. The incom-ing direction of the primary particle defines two regions, “early”( | ζ | < π/ ) and “late” region ( | ζ | > π/ ). Note the differentamount of atmosphere traversed by the particles reaching the detec-tors in each region. netic and muonic components of extensive air showers witha duty cycle of nearly 100%. Each water-Cherenkov unit isa 1.2 m depth, 10 m area, detector containing 12000 litersof ultra-pure water. The water volume is viewed by three9” photomultiplier tubes (PMTs). Two signals (from the an-ode and from the amplified dynode) from each of PMTs aredigitized by 40 MHz 10-bit Flash Analog to Digital Convert-ers (FADCs). The recorded signals are calibrated in units ofthe signal produced by a muon traversing the water vertically.The unit is termed the “Vertical Equivalent Muon” or VEM[17]. The shower-trigger requirement is based on a 3-fold co-incidence, satisfied when a triangle of neighboring stations istriggered [18]. These triggers result in the recording of . µ s(in 768 bins) of data from each of the six FADCs in each trig-gered station. In the present analysis, that relies on the useof the risetime of the signals (see section IV), we use FADCtraces from stations in events that are well-confined withinthe array, that is, the largest signal station is surrounded by6 working stations, so that an accurate reconstruction is en-sured. For these events, we determine the arrival directions ofthe primary cosmic rays from the relative arrival times of theshower front in the triggered stations. The angular resolutionis 0.9 ◦ for energies above × eV [19]. The estimator ofthe primary energy is the reconstructed signal at 1000 m fromthe shower core, S (1000) . This is determined, together withthe core position, through a fit of the recorded signals (con-verted to units of VEM after integration of the FADC traces)to a lateral distribution function that describes the average ratefall-off of the signal as a function of the distance from theshower core. For S (1000) > VEM (corresponding to pri-mary energy around × eV) the core location is deter-mined with an uncertainty of 50 m, which is independent ofthe shower geometry [12, 20]. The accuracy of the determina-tion of S (1000) is 12% (3%) at × ( ) eV [21].The conversion from this estimator to energy is derivedthrough the use of a subset of showers that trigger the fluores-cence detector and the surface array independently (“hybrid”events). The statistical uncertainty in the energy determina-tion is about 16% (12%) for energies above × ( ) eV. The absolute energy scale, determined by the FD, has asystematic uncertainty of 14% [22]. In the following we useevents for which the zenith angle is less than 62 ◦ and the en-ergy is above × eV: the efficiency of detection in suchcases is 100%.The fluorescence detector consists of 27 optical telescopesthat overlook the array [23, 24]. On clear moonless nights,these are used to observe the longitudinal development ofshowers by detecting the fluorescence light produced in theatmosphere by charged particles along the shower trajectory.The duty cycle of the FD is ∼ ◦ . With the help of in-formation from atmospheric monitoring devices [25] the lightcollected by the telescopes is corrected for the atmospheric at-tenuation between the shower and the detector. Finally, fromthe shower geometry the longitudinal shower profile is recon-structed from the light recorded by the FD [5, 15, 16]. The X max value and the energy are determined by fitting the re-constructed longitudinal profile with a Gaisser-Hillas function[26]. The resolution of X max is around 20 g cm − in the en-ergy range of interest for this work. III. CONCEPT OF AZIMUTHAL ASYMMETRY IN THERISETIME
The water-Cherenkov detectors are used to measure the sig-nal size and the spread in arrival times of the signals producedby the different components of an extensive air shower. Anapproach originally used to analyze the data of the HaverahPark detector [27] showed that observables related to time-spread have sensitivity to the mass of the primary particle. Incomposition studies, the risetime, t / , is usually employedto characterize the recorded signal. It is defined as the timeof increase from 10% to 50% of the total integrated signal.The average risetime is a function of the distance to the axisof the shower and of the zenith angle of that shower. In in-dividual events it is necessary to take account of the time atwhich each detector is struck. Note that detectors that arehit later will register the shower after it has passed throughadditional atmosphere, and the particles detected, in particu-lar the muons, will in general come from a smaller angle tothe shower axis. To describe this we introduce the conceptof “early” and “late” detectors (see Fig. 1). We classify as“early” those detectors that record the passage of the showerfront first. With our convention these correspond to detectorswith polar angles | ζ | < π/ with respect to the direction ofthe shower axis projected on to the ground. Detectors in the | ζ | > π/ region are dubbed “late”.The top two panels of Fig. 2 show the recorded signals for anearly vertical event in an early station (left) and a late station(right) (the reconstructed zenith angle is 15.7 ◦ ). The FADCtraces can, to a good approximation, be considered equal inamplitude and time-spread. The bottom panels of Fig. 2 showtwo typical FADC signals recorded for an event with a recon-structed energy of 7.7 EeV and a zenith angle of 52 ◦ (early and t [ns]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 S i gn a l [ VE M ] S = 35.3 VEMr = 1312.2 m = 653 ns t = 30.6 ζ t [ns]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 S i gn a l [ VE M ] S = 32.8 VEMr = 1339.7 m = 654 ns t = 172.7 ζ t [ns]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 S i gn a l [ VE M ] S = 22.7 VEMr = 1274.7 m = 436 ns t = 27.4 ζ t [ns]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 S i gn a l [ VE M ] S = 9.9 VEMr = 1264.2 m = 128 ns t = 171 ζ FIG. 2. Top: two stations in an event of 16.9 EeV and 15.7 ◦ in zenith. Bottom: two stations in an event of 7.7 EeV and 52 ◦ in zenith. Leftpanels correspond to early stations while right panels correspond to late stations. late as above). In this event, although both detectors are lo-cated at similar distances from the shower core, the traces arestrikingly different, both in magnitude and time structure. Weobserved this asymmetric behavior (in total signal and time-spread) for the first time in the FADC traces recorded with thedetectors of the Engineering Array constructed for the Obser-vatory [28].To appreciate the origin of the asymmetries, we have to un-derstand the behavior of the copious number of muons andelectromagnetic particles that reach the ground. For a verticalshower of 10 EeV a signal of ∼
50 VEM is recorded at 1000m from the shower axis. About 50% of the total signal is dueto muons sufficiently energetic to traverse the detector with-out stopping. Electrons are a factor 10, and photons a factor100, more numerous than muons. They make up the other50% of the total signal and, as they have average energiesof ∼
10 MeV [29], are largely absorbed in the 3.2 radiationlengths of water in the station. The ratio of the muon to elec-tromagnetic signal changes with distance and zenith angle ina manner that is known from dedicated measurements madeat several of the early ground-detector arrays. Greisen [30]was the first to point out that attenuation of shower particlesin the atmosphere would lead to a loss of circular symmetryin the signal intensities recorded by a detector at a single at-mospheric depth. Experimental evidence of this effect wasobtained by England [31] using data from Haverah Park. Re-garding the risetime of the signals, Linsley and Scarsi [32]demonstrated that the thickness of the disc of particles in theshower increased from a few meters near the axis to several hundreds of meters at large distances. Using Haverah Parkdata, a study showed that the spread of the arrival time distri-bution was decreased by attenuation across the array [33].The observed azimuthal asymmetry is due to two effects.On the one hand, a contribution comes from the quenching ofthe electromagnetic signal. Since the particles that reach latedetectors traverse longer atmospheric paths, we expect a big-ger attenuation of electrons and photons as compared to earlydetectors. On the other hand, there are also contributions tothe asymmetry from geometrical effects. In this case, not onlyis the electromagnetic component important, but muons alsoplay a role. The cylindrical design of the the detectors affordslonger possible paths within the detector at larger zenith an-gles, thus increasing the signal strength from muons and com-pensating somewhat for the reduced numbers of electrons andphotons. The angular distributions of detected muons are dif-ferent for higher zenith angle showers, as late detectors recordmore muons emitted closer to the shower axis. Geometricaleffects predominate at small zenith angles, while for showerswith θ > ◦ attenuation effects are the main contribution.As already mentioned, it is known that the risetime has adependence with respect to the distance of the detector to thecore of the shower in the plane of the shower front, r [27].Fig. 3 shows that t / is an increasing function of distance.For the range of distances selected in this work, this functioncan be approximated to first order as a straight line. But therisetime is not the only observable showing a distance depen-dence. Based on the previous considerations we expect thatthe asymmetry will also show a dependence on core distance. r [m]600 800 1000 1200 1400 1600 1800 2000 [ n s ] / t [ n s ] 〉 / t 〈 FIG. 3. Example of risetime vs core distance for stations in eventsbetween energies 10 . − . eV and zenith angle 42 ◦ − ◦ .Top: scatter distribution of the risetime values for individual stations.Bottom: bin-by-bin averages of the risetime. Vertical bars representthe root-mean-square of the corresponding distributions. For measurements close to the shower axis, the path differencebetween late and early detectors is not large and therefore wedo not expect a sizeable asymmetry. It becomes more evidentas the distance increases.The azimuthal asymmetry of the risetime must also dependon the zenith angle. As suggested earlier in Fig. 2, no asym-metry is expected for vertical showers but it is expected togrow as the zenith angle increases (and therefore differencesin atmospheric paths become larger for a given set of trig-gered detectors). However this trend reaches a point where itdoes not hold for more horizontal events. For these the elec-tromagnetic signal is quenched due to the longer atmosphericpath travelled and the particles in the showers are dominantlymuons. This translates into a reduction of the asymmetry as θ approaches 90 ◦ . As discussed in [34, 35], for a given energy E , the azimuthal asymmetry dependence upon sec θ shows acorrelation with the average longitudinal development of theshower. Hence the time asymmetry is sensitive to the averagemass of the primary cosmic ray. IV. AZIMUTHAL ASYMMETRY USING AUGER DATAA. The analysis
The first step in the analysis is the measure of the t / valuein each detector. We use the events collected with the sur-face array of the Pierre Auger Observatory from January 2004to October 2014. We consider only the FADC traces of theevents that pass the selection criteria described in section II.Those traces allow us to compute the average of the risetimesof active PMTs in every station. Quality cuts on data havebeen applied, based on core distance and total recorded sig-nal. We have required that the recorded signal is larger than (deg) ζ -150 -100 -50 0 50 100 150 [ n s / m ] 〉 / r / t 〈 (deg) θ /ndf χ log(E/eV) = 18.55 - 18.70 [deg] ζ -150 -100 -50 0 50 100 150 [ n s / m ] 〉 / r / t 〈 [deg] θ /ndf χ log(E/eV) = 19.20 - 19.50 FIG. 4. Dependence of (cid:104) t / /r (cid:105) on the polar angle ζ in the showerplane for primary energy log ( E /eV) = 18.55 − −
10 VEM, above which level the probability of single detectortriggering is about 100 % [18]. With respect to core position,detectors used for the analysis were required to be further than500 m from the core of the shower to avoid signal saturationeffects that prevent an accurate measurement of t / (signalssaturate at average values of about 800 VEM depending onthe PMT gains and the risetime of the signal). The uncer-tainty of the measured risetimes is estimated comparing mea-surements of the same parameter from multiple observations:twins (stations separated by 11 m) or stations belonging tothe same event with core distance difference smaller than 100m [36, 37]. It is required that the water-Cherenkov detectorsare within 2 km of the core: this is a fiducial cut to excludestations with high uncertainties in the reconstructed risetimes.After application of the station selection criteria, a total of191534 FADC signals from 54584 events remain.The second step consists in measuring the azimuthal asym-metry of the risetime distributions as a function of the polarangle, for fixed energies and zenith angles. This measurementcannot be done on a shower-by-shower basis because it is notpossible to sample the whole range of the polar angle, fromearly to late regions, in a single event. Thus, a statistical ap-proach is applied to characterize the azimuthal asymmetry ofthe risetime as a function of the polar angle, using all the sta-tions from the events at a given energy and zenith angle.The risetime grows with the core distance r , and in a firstapproximation, follows a linear behavior in the range of dis-tances considered in the present analysis as was seen in Fig. 3.The variable used to study the azimuthal asymmetry is t / /r .This quantity is chosen since an average value using all sta-tions at different core distances, allowing an increase in thenumber of events used, can be computed and thus the asym-metry information from the whole r range can be used in theanalysis. To derive the behavior of the asymmetry vs polar an-gle we thus use the value (cid:104) t / /r (cid:105) averaged over all stationsin all events that fulfill the criteria described above in definedbins of energy and angle.As an example, we show in Fig. 4 the values of (cid:104) t / /r (cid:105) vs ζ for eight zenith angles and for a narrow interval of energycentered on . × eV (top panel) and on . × eV(bottom panel). For each zenith-angle band the data are fittedto the function (cid:104) t / /r (cid:105) = a + b cos ζ + c cos ζ . The asym-metry with respect to ζ is evident and the ratio b/ ( a + c ) , theso-called asymmetry factor, is used to give a measure of theasymmetry. In Fig. 4 results for a wide range of zenith an-gles are shown although the analysis has been restricted to theinterval 30 ◦ − ◦ .As mentioned before the asymmetry depends on the dis-tance to the core position. To take that into account the analy-sis has been carried out independently for two r -intervals, i.e.,500 − − − − (cid:104) t / /r (cid:105) vs ζ is displayed for both core distance intervals for showerswith log( E /eV) = 19.1 and θ = 51 ◦ . The smaller asymmetryamplitude of the 500 − sec θ . In Figs. 6 and 7, b/ ( a + c ) has been plottedversus ln(sec θ ) for six energy bins and for both core distanceintervals. It is evident that for a given primary energy, theazimuthal asymmetry depends on zenith angle of the primarycosmic ray. (deg) ζ -150 -100 -50 0 50 100 150 [ n s / m ] 〉 / r / t 〈
500 - 1000 m1000 - 2000 m
500 - 1000 m: 0.002 ± a = 0.164 0.002 ± b = 0.042 0.003 ± c = 0.009 /ndf = 0.81 χ ± a = 0.160 0.002 ± b = 0.063 0.004 ± c = 0.016 /ndf = 0.83 χ FIG. 5. Dependence of (cid:104) t / /r (cid:105) on ζ for two chosen core distance in-tervals for data. Results of the fitted parameters (see text) are shownfor each core distance interval. For each energy interval, the dependence of the asymme-try parameter on ln(sec θ ) is fitted using a Gaussian function.From this fit we can determine the value of ln(sec θ ) for whichthe asymmetry parameter maximizes, and the corresponding (sec θ ) max value will be used as the observable to describe thelongitudinal evolution of the shower and thus with capabilityfor the analysis of the mass composition.The dependence of the asymmetry on the core distanceleads to a dependence of (sec θ ) max on the r interval of the sta-tion sample used in the analysis, as we can see in Figs. 6 and 7.Apart from geometrical effects this can be understood as fol-lows. Closer to the shower core (500 − − − (sec θ ) max values as expected since closer tothe core the asymmetry is smaller, and thus, the zenith an-gle at which the muon component starts to dominate (and theasymmetry starts to decrease) is higher. B. Systematic Uncertainties
The sources of systematic uncertainties related to the preci-sion with which the absolute value of (sec θ ) max can be mea-sured are discussed in the following. Results are presented inunits of (sec θ ) max which has a typical value of ∼ Risetime uncertainties . A source of systematic uncertaintyis that from the determination of the risetime itself. To evalu-ate the effect of this uncertainty, the risetime has been shiftedrandomly around a Gaussian distribution with standard devi- )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.6 ± = 1.551 max ) θ sec( /ndf 10 / 7 χ Prob 0.19 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.8 ± = 1.568 max ) θ sec( /ndf 8.6 / 7 χ Prob 0.28 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.9 ± = 1.570 max ) θ sec( /ndf 1.2 / 7 χ Prob 0.99 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.1 ± = 1.580 max ) θ sec( /ndf 7.1 / 7 χ Prob 0.42 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.3 ± = 1.567 max ) θ sec( /ndf 6.8 / 7 χ Prob 0.45 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.6 ± = 1.589 max ) θ sec( /ndf 25 / 7 χ Prob 0.00087
FIG. 6. Asymmetry longitudinal development in bins of log (
E/eV ) at the interval 500 − . − . , . − . , . − . , . − . , . − . and above . . ation σ given by the uncertainty in the measurement of therisetime as mentioned in section IV A. A systematic uncer- tainty of +0 . / − . is obtained for the 500 − +0 . / − . for the 1000 − )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.6 ± = 1.526 max ) θ sec( /ndf 13 / 7 χ Prob 0.069 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.8 ± = 1.523 max ) θ sec( /ndf 10 / 7 χ Prob 0.18 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 18.9 ± = 1.529 max ) θ sec( /ndf 17 / 7 χ Prob 0.015 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.1 ± = 1.533 max ) θ sec( /ndf 7.3 / 7 χ Prob 0.40 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.3 ± = 1.521 max ) θ sec( /ndf 8.5 / 7 χ Prob 0.29 )) θ ln(sec(0.2 0.3 0.4 0.5 0.6 0.7 A sy mm e t r y F ac t o r log(E/eV) = 19.6 ± = 1.526 max ) θ sec( /ndf 7.3 / 7 χ Prob 0.40
FIG. 7. Asymmetry longitudinal development in bins of log (
E/eV ) at the interval 1000 − . − . , . − . , . − . , . − . , . − . and above . . val. Risetime parametrization . The use of different parametriza-tions in the dependency of the risetime with the distance to the1core is another possible source of uncertainty in (sec θ ) max .The dependence of the results on the particular choice of func-tion has been checked by replacing the linear function used inthe analysis by a quadratic function. This implies a redef-inition of the parameter, using then (cid:104) t / /( a + b r + c r ) (cid:105) instead of (cid:104) t / / r (cid:105) . The estimated systematic uncertaintiesare +0 . / − . for the interval 500 − +0 . / − . for the interval 1000 − Selection efficiency . To evaluate a potential bias of the re-sults towards a particular nuclear composition, we producedMonte Carlo samples of mixed composition (25% p − −
50% Fe and 75% p −
25% Fe) with bothhadronic models QGSJETII-04 and EPOS-LHC. The sampleswere analyzed and the results were compared with the knowninput composition. The maximum deviations correspond tothe 50% −
50% composition and are taken as a systematic un-certainty. The values are of ± Core position reconstruction . The systematic uncertaintyarising from the reconstruction of the shower core was de-termined by shifting in the late direction (see section III) theposition of the core by 50 m, corresponding to the typical shiftto the early regions in inclined showers due to the asymmetryin the signal intensity. The whole chain of analysis to obtainthe new values of the position of the maximum of the asym-metry was repeated. The systematic uncertainty in units of (sec θ ) max are +0 . / − . for the 500 − +0 / − . for the 1000 − Energy scale . The absolute energy calibration of the Ob-servatory is affected by a total systematic uncertainty of 14 % [22]. To study the corresponding effect on (sec θ ) max , the en-ergy values assigned to each event were shifted by the corre-sponding percentage and the full chain of the analysis was re-peated. The shift leads to an uncertainty of +0 . / − . for the 500 − +0 . / − . in unitsof (sec θ ) max for the 1000 − Additional Cross-Checks . The systematic uncertainties es-timated above have been validated by performing numerouscross-checks on the stability of the results. The most sig-nificant studies are: i) a potential dependence on (sec θ ) max due to the selection cuts in the signal intensity was studiedby shifting the upper and lower cuts in the signal size; ii)the effect of the cuts on the angular intervals of the samplewas also studied by varying the angular limits of the nomi-nal interval; iii) the lateral width of the shower (in particularof the electromagnetic component) depends on pressure andtemperature. A possible bias affecting the risetime measure-ments and hence (sec θ ) max was evaluated splitting the datainto “hot” (summer and spring) and “cold” (winter and au-tumn) periods and repeating the whole analysis chain for eachcase. iv) possible effect of aging [12, 38] of the SD detectorson the results were studied separating the data sample in twoequal sets, “old” (Jan.2004 − Jan.2011) and “new” (Jan.2011 − Oct.2014). The first i) and ii) studies yield a maximumvariation of (sec θ ) max of 0.0044 which is well within the sys-tematic uncertainties. In the case of iii) and iv) differencesare compatible with zero within the statistical uncertainties ofeach sample. E [eV] m ax ) q ( sec FIG. 8. Energy dependence of (sec θ ) max for both intervals of coredistance 500 − − The overall systematic uncertainty (see Table I) in each ra-dial interval amounts to +0 . / − . for the 500 − +0 . / − . for the 1000 − log( E /eV)= 19.1 and 500 − (sec θ ) max = 1.580 ± +0 . − . (sys), while for the 1000 − (sec θ ) max = 1.533 ± +0 . − . (sys).Our analysis is therefore dominated by systematic uncertain-ties. Source of systematic 500 − − Risetime uncertainties +0 . − . . − . Risetime parametrization +0 . − . . − . Selection efficiency +0 . − .
010 +0 . − . Core position reconstruction +0 . − . − . Energy scale +0 . − . . − . Total systematic value + − + − TABLE I. Contributions to systematic uncertainty of (sec θ ) max forall sources in both core distance intervals. Values are summed inquadrature to obtain the final systematic result. V. RESULTS
Once the value of (sec θ ) max for each energy bin has beenobtained in each core distance interval, we can perform the2final step of the asymmetry analysis, that is, the evaluation ofthe dependence of (sec θ ) max on the primary energy. In Fig. 8this result for both r intervals is shown.To extract mass estimates from the measurements one mustrely on the comparison with predictions made using currentmodels of hadronic interactions extrapolated to these energies.For this purpose, a library of Monte Carlo events generatedwith the CORSIKA code [39] has been produced using theEPOS-LHC and QGSJETII-04 hadronic interaction modelsfor two different primary species: proton and iron. A total of77000 events (38500 of each primary) have been produced foreach interaction model. The log( E /eV) values ranged from18.00 to 20.25 in bins of 0.25 with eleven discrete zenith an-gles between 18 ◦ and 63 ◦ .Note that, in principle, the dependence of the (sec θ ) max on E with the radial interval shown in Fig. 8 should not limitthe capability of the asymmetry method for mass analysis pro-vided Monte Carlo simulations are able to correctly reproducethis dependence.The comparison of the energy dependence of the measured (sec θ ) max with predictions for proton and iron primaries, andfor both hadronic models, is shown in Fig. 9. The system-atic uncertainty on the measured (sec θ ) max is 16 % (500 − % (1000 − (sec θ ) max for both models. Fromthis figure it is evident that the Auger data are bracketed byproton and iron in both models, independent of the core dis-tance interval studied. However, the dependence of (sec θ ) max on energy is such that it is difficult to draw strong conclusionsas rather different predictions come from the two models, par-ticularly in the larger distance interval. However, in both casesthere is an indication that the mean mass increases slowly withenergy in line with other Auger studies [5, 13].It is also evident from these plots that the mass predictionsdepend strongly on the hadronic model adopted. To studythese discrepancies further, we have transformed the measure-ments of (sec θ ) max (and their corresponding uncertainties)into mass units.For each interaction model, the value of (cid:104) ln A (cid:105) derived fromdata has been computed using the following relationships: ln A = (sec θ ) max;p − (sec θ ) max;data (sec θ ) max;p − (sec θ ) max;Fe · ln 56 (1) ∆ ln A = − ∆(sec θ ) max;data (sec θ ) max;p − (sec θ ) max;Fe · ln 56 (2)The result of this transformation is shown in Fig. 10. Whilefor the EPOS-LHC model the mean mass is independent ofthe radial interval used in the analysis, as expected, this ismuch less evident for the QGSJETII-04 model. These resultsimply that the study of (sec θ ) max can also be used to probethe validity of hadronic interaction models. E [eV] m ax ) θ ( sec pFe 500 - 1000 m E [eV] m ax ) θ ( sec pFe 1000 - 2000 m FIG. 9. Comparison between (sec θ ) max , for both data and MonteCarlo predictions in the 500 − − VI. COMPARISON WITH PREVIOUS MEASUREMENTSAND CONCLUSIONS
The azimuthal dependence of the t / values obtained fromabout × FADC traces registered by the SD detector ofthe Pierre Auger Observatory has been used to obtain a mass-sensitive parameter, (sec θ ) max . The evolution of this parame-ter as a function of energy, above × eV, has been studiedin two ranges of core distance interval. The comparison withpredictions from the most up-to-date hadronic models, EPOS-LHC and QGSJETII-04, although hinting at a transition from3 E [eV] æ l n A Æ -1012345 æ l n A Æ -1012345 FIG. 10. Comparison of (cid:104) ln A (cid:105) as a function of energy for bothcore distance intervals predicted by EPOS-LHC (top panel) andQGSJETII-04 (bottom panel). lighter to heavier composition as the energy increases, doesnot allow us to draw strong conclusions on its absolute value.This is because the predictions are at variance not only withthe two models, but even with the two distance ranges. Inparticular, the comparison between data and predictions fromQGSJETII-04 suggests unphysical conclusions, with the massseemingly dependent upon the distance of the stations fromthe core. This is a clear indication that further deficiencies inthe modelling of showers must be resolved before (sec θ ) max can be used to make inferences about mass composition. It also shows that the reach of the (sec θ ) max observable extendsto providing a test of hadronic interactions models.We conclude by making a comparison in Fig. 11 of massvalues (in terms of (cid:104) ln A (cid:105) ) obtained from the measurementsof (sec θ ) max for the two distance ranges to previous massestimates from the Pierre Auger Observatory [5, 13]. Thethree mass measurements have different systematic uncertain-ties and are sensitive to very different types of hadronic in-teractions since the importance of the muonic shower compo-nent is different within each of them. In the direct determina-tion of X max [5], the dominant shower component is the elec-tromagnetic one and the proportion of muons in the showeris of minor importance. As a consequence in that case thedominant contribution comes from the very first high energyhadronic interactions [40]. By contrast, the muon production-depth [13] is dominated by the muon component which is theresult of a long cascade of lower energy hadronic interactions(mostly pion-nucleus interactions) [41]. The asymmetry inthe risetime is associated with a complex interplay betweenthese two components. As these three measurements lead todiscordant estimates of (cid:104) ln A (cid:105) , it is impossible to concludewhich of the two models considered here best describes thetotality of the data. While the EPOS model yields resultsthat are consistent at different distances (Fig. 10) for instance,the mass values predicted from the muon production-depth(Fig. 11) would imply that trans-uranic elements are domi-nant above 20 EeV. The (cid:104) X µ max (cid:105) result, and a related analysisof muons in very inclined showers made at the Auger Obser-vatory [42], suggest that the muon component of showers isincorrectly modelled. In particular, the measured pion-carboncross-section for the production of a forward ρ meson, whichdecays to two charge pions, instead of π as leading particleexceeds what has been included in the models [43] and workis underway to evaluate the importance of this effect on muonproduction and MPD. Moreover the lack of measurements ofthe production of forward baryons in pion-nucleus interac-tions, which also has a large effect on muon production [44]and on (cid:104) X µ max (cid:105) [41], leads to large uncertainties in model pre-dictions. Additionally one must not overlook the possibilitythat a new phenomenon, such as described in [45, 46], couldbecome important at the energies studied here which explorethe centre-of-mass region well above that studied directly atthe LHC. Discriminating between such possibilities is a targetof the AugerPrime project [47] which will have the ability toseparate the muon and electromagnetic signals. ACKNOWLEDGMENTS
The successful installation, commissioning, and operationof the Pierre Auger Observatory would not have been possiblewithout the strong commitment and effort from the technicaland administrative staff in Malarg¨ue. We are very grateful tothe following agencies and organizations for financial support:Comisi´on Nacional de Energ´ıa At´omica, Agencia Na-cional de Promoci´on Cient´ıfica y Tecnol´ogica (ANPCyT),Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas(CONICET), Gobierno de la Provincia de Mendoza, Mu-4
E [eV] 〉 l n A 〈 〉 max X 〈 max ) θ (sec 〉 µ max X 〈 FepEPOS-LHC 500-1000 m
E [eV] 〉 l n A 〈 〉 max X 〈 max ) θ (sec 〉 µ max X 〈 FepQGSJETII-04 500-1000 m
E [eV] 〉 l n A 〈 〉 max X 〈 max ) θ (sec 〉 µ max X 〈 FepEPOS-LHC 1000-2000 m
E [eV] 〉 l n A 〈 〉 max X 〈 max ) θ (sec 〉 µ max X 〈 FepQGSJETII-04 1000-2000 m
FIG. 11. (cid:104) ln A (cid:105) as a function of energy as predicted by EPOS-LHC and QGSJETII-04. Results from the asymmetry analysis in both r intervalsare shown and compared with those from the elongation curve [5] and the MPD method [13]. nicipalidad de Malarg¨ue, NDM Holdings and Valle LasLe˜nas, in gratitude for their continuing cooperation overland access, Argentina; the Australian Research Coun-cil; Conselho Nacional de Desenvolvimento Cient´ıfico eTecnol´ogico (CNPq), Financiadora de Estudos e Projetos(FINEP), Fundac¸ ˜ao de Amparo `a Pesquisa do Estado deRio de Janeiro (FAPERJ), S˜ao Paulo Research Foundation(FAPESP) Grants No. 2010/07359-6 and No. 1999/05404-3, Minist´erio de Ciˆencia e Tecnologia (MCT), Brazil; GrantNo. MSMT-CR LG13007, No. 7AMB14AR005, and theCzech Science Foundation Grant No. 14-17501S, Czech Re-public; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientifique (CNRS), Conseil R´egional Ile-de-France, D´epartement Physique Nucl´eaire et Corpusculaire(PNC-IN2P3/CNRS), D´epartement Sciences de l’Univers(SDU-INSU/CNRS), Institut Lagrange de Paris (ILP) GrantNo. LABEX ANR-10-LABX-63, within the Investisse-ments d’Avenir Programme Grant No. ANR-11-IDEX-0004-02, France; Bundesministerium f¨ur Bildung und Forschung(BMBF), Deutsche Forschungsgemeinschaft (DFG), Fi-nanzministerium Baden-W¨urttemberg, Helmholtz Alliancefor Astroparticle Physics (HAP), Helmholtz-GemeinschaftDeutscher Forschungszentren (HGF), Ministerium f¨ur Wis-senschaft und Forschung, Nordrhein Westfalen, Minis-5terium f¨ur Wissenschaft, Forschung und Kunst, Baden-W¨urttemberg, Germany; Istituto Nazionale di Fisica Nu-cleare (INFN),Istituto Nazionale di Astrofisica (INAF),Ministero dell’Istruzione, dell’Universit´a e della Ricerca(MIUR), Gran Sasso Center for Astroparticle Physics (CFA),CETEMPS Center of Excellence, Ministero degli Affari Es-teri (MAE), Italy; Consejo Nacional de Ciencia y Tecnolog´ıa(CONACYT), Mexico; Ministerie van Onderwijs, Cultuuren Wetenschap, Nederlandse Organisatie voor Wetenschap-pelijk Onderzoek (NWO), Stichting voor Fundamenteel On-derzoek der Materie (FOM), Netherlands; National Cen-tre for Research and Development, Grants No. ERA-NET-ASPERA/01/11 and No. ERA-NET-ASPERA/02/11, Na-tional Science Centre, Grants No. 2013/08/M/ST9/00322,No. 2013/08/M/ST9/00728 and No. HARMONIA 5 –2013/10/M/ST9/00062, Poland; Portuguese national fundsand FEDER funds within Programa Operacional Factoresde Competitividade through Fundac¸ ˜ao para a Ciˆencia ea Tecnologia (COMPETE), Portugal; Romanian Authority for Scientific Research ANCS, CNDI-UEFISCDI partner-ship projects Grants No. 20/2012 and No. 194/2012, GrantsNo. 1/ASPERA2/2012 ERA-NET, No. PN-II-RU-PD-2011-3-0145-17 and No. PN-II-RU-PD-2011-3-0062, the Minis-ter of National Education, Programme Space Technologyand Advanced Research (STAR), Grant No. 83/2013, Roma-nia; Slovenian Research Agency, Slovenia; Comunidad deMadrid, FEDER funds, Ministerio de Educaci´on y Ciencia,Xunta de Galicia, European Community 7th Framework Pro-gram, Grant No. FP7-PEOPLE-2012-IEF-328826, Spain; Sci-ence and Technology Facilities Council, United Kingdom;Department of Energy, Contracts No. DE-AC02-07CH11359,No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 andNo. DE-SC0011689, National Science Foundation, GrantNo. 0450696, The Grainger Foundation, USA; NAFOSTED,Vietnam; Marie Curie-IRSES/EPLANET, European Parti-cle Physics Latin American Network, European Union 7thFramework Program, Grant No. PIRSES-2009-GA-246806;and UNESCO. [1] J. Linsley, L. Scarsi, and B. Rossi, Phys. Rev. Lett. , 485(1961).[2] R. U. Abbasi et al. (HiRes), Phys. Rev. Lett. , 101101(2008), arXiv:astro-ph/0703099 [astro-ph].[3] J. Abraham et al. (Pierre Auger), Phys. Rev. Lett. , 061101(2008), arXiv:0806.4302 [astro-ph].[4] M. Tueros (Pierre Auger), in Proceedings, 33rd InternationalCosmic Ray Conference, Rio de Janeiro, Brazil (2013) p. 0705.[5] A. Aab et al. (Pierre Auger), Phys. Rev.
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