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
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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)
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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
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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
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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].
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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.
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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.
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