Measurement of the Depth of Maximum of Extensive Air Showers above 10(18) eV

TLDR: The measurement of the depth of maximum, X{max}, of the longitudinal development of air showers induced by cosmic rays is described and the interpretation of these results in terms of the cosmic ray mass composition is briefly discussed.

Abstract: We describe the measurement of the depth of maximum, Xmax, of the longitudinal development of air showers induced by cosmic rays. Almost four thousand events above 10^18 eV observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of (106 +35/-21) g/cm^2/decade below 10^(18.24 +/- 0.05) eV and (24 +/- 3) g/cm^2/decade above this energy. The measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm^2. The interpretation of these results in terms of the cosmic ray mass composition is briefly discussed.

Figures

FIG. 2. hXmaxi as a function of energy. Lines denote a fit with a broken line in lgE. The systematic uncertainties of hXmaxi 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.

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.

FIG. 3. hXmaxi and rmsðXmaxÞ compared with air shower simulations [20] using different hadronic interaction models [21].

Full text

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
http://link.aps.org/doi/10.1103/PhysRevD.62.093023
http://hdl.handle.net/2440/61284
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13
th
May 2013

Measurement of the Depth of Maximum of Extensive Air Showers above 10
18
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-Mun
˜
iz,
8
M. Ambrosio,
9
L. Anchordoqui,
10
S. Andringa,
2
T. Antic
ˇ
ic
´
,
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. Ba
¨
cker,
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. Belle
´
toile,
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. Blu
¨
mer,
34,16
M. Boha
´
c
ˇ
ova
´
,
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. Conceic¸a
˜
o,
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. Dı
´
az 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. Filipc
ˇ
ic
ˇ
,
66,52
I. Fleck,
19
S. Fliescher,
60
C. E. Fracchiolla,
26
E. D. Fraenkel,
58
U. Fro
¨
hlich,
19
W. Fulgione,
3
R. F. Gamarra,
45
S. Gambetta,
67
B. Garcı
´
a,
1
D. Garcı
´
aGa
´
mez,
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. Go
´
mez Berisso,
6
P. Gonc¸alves,
2
D. Gonzalez,
34
J. G. Gonzalez,
40,69
D. Go
´
ra,
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. Ho
¨
randel,
47
A. Horneffer,
47
M. Hrabovsky
´
,
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. Ke
´
gl,
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. Kro
¨
mer,
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. Lea
˜
o,
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. Lo
´
pez,
78
A. Lopez Agu
¨
era,
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. Martı
´
nez 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. Mic
ˇ
anovic
´
,
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. Mostafa
´
,
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. Noz
ˇ
ka,
35
M. Nyklicek,
35
J. Oehlschla
¨
ger,
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. Rivie
`
re,
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. Rodrı
´
guez-Frı
´
as,
32
G. Ros,
32
J. Rosado,
13
T. Rossler,
74
M. Roth,
16
B. Rouille
´
-d’Orfeuil,
17,5
E. Roulet,
6
A. C. Rovero,
89
F. Salamida,
16,75
H. Salazar,
78,90
G. Salina,
36
F. Sa
´
nchez,
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
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week ending
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0031-9007=10=104(9)=091101(7) 091101-1 Ó 2010 The American Physical Society

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. Schova
´
nek,
35
F. Schroeder,
16
S. Schulte,
60
F. Schu
¨
ssler,
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. S
´
miałkowski,
68
R. S
ˇ
mı
´
da,
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. Suomija
¨
rvi,
59
A. D. Supanitsky,
54
T. S
ˇ
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ˇ
a,
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. Tas
¸
ca
˘
u,
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. Tome
´
,
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. Valde
´
s Galicia,
54
I. Valin
˜
o,
16
L. Valore,
9
A. M. van den Berg,
58
J. R. Va
´
zquez,
13
R. A. Va
´
zquez,
8
D. Veberic
ˇ
,
52,66
T. Venters,
17
V. Verzi,
36
M. Videla,
1
L. Villasen
˜
or,
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. Wilczyn
´
ska,
37
H. Wilczyn
´
ski,
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. Ziolkowski
19
(Pierre Auger Collaboration)
1
National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina
2
LIP and Instituto Superior Te
´
cnico, Lisboa, Portugal
3
Istituto di Fisica dello Spazio Interplanetario (INAF), Universita
`
di Torino and Sezione INFN, Torino, Italy
4
Fermilab, Batavia, Illinois, USA
5
Laboratoire AstroParticule et Cosmologie (APC), Universite
´
Paris 7, CNRS-IN2P3, Paris, France
6
Centro Ato
´
mico 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
Universita
`
di Napoli ‘‘Federico II’’ and Sezione INFN, Napoli, Italy
10
University of Wisconsin, Milwaukee, Wisconsin, USA
11
Rudjer Bos
ˇ
kovic
´
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 Nucle
´
aire et de Hautes Energies (LPNHE), Universite
´
s Paris 6 et Paris 7, CNRS-IN2P3, Paris, France
16
Karlsruhe Institute of Technology—Campus North—Institut fu
¨
r Kernphysik, Karlsruhe, Germany
17
University of Chicago, Enrico Fermi Institute, Chicago, Illinois, USA
18
Pierre Auger Southern Observatory and Comisio
´
n Nacional de Energı
´
a Ato
´
mica, Malargu
¨
e, Argentina
19
Universita
¨
t Siegen, Siegen, Germany
20
IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
21
Karlsruhe Institute of Technology—Campus North—Institut fu
¨
r 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 Universita
¨
t Wuppertal, Wuppertal, Germany
29
Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universite
´
Joseph Fourier, INPG, CNRS-IN2P3, Grenoble, France
30
University of Wisconsin, Madison, Wisconsin, USA
31
Max-Planck-Institut fu
¨
r Radioastronomie, Bonn, Germany
32
Universidad de Alcala
´
, Alcala
´
de Henares (Madrid), Spain
33
Dipartimento di Fisica dell’Universita
`
del Salento and Sezione INFN, Lecce, Italy
34
Karlsruhe Institute of Technology—Campus South—Institut fu
¨
r Experimentelle Kernphysik (IEKP), Karlsruhe, Germany
35
Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic
36
Universita
`
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
PRL 104, 091101 (2010)
PHYSICAL REVIEW LETTERS
week ending
5 MARCH 2010
091101-2

41
Case Western Reserve University, Cleveland, Ohio, USA
42
Universita
`
di Catania and Sezione INFN, Catania, Italy
43
Universita
`
di Torino and Sezione INFN, Torino, Italy
44
Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil
45
Centro Ato
´
mico Constituyentes (Comisio
´
n Nacional de Energı
´
a Ato
´
mica/CONICET/UTN-FRBA), Buenos Aires, Argentina
46
Pierre Auger Southern Observatory, Malargu
¨
e, Argentina
47
IMAPP, Radboud University, Nijmegen, Netherlands
48
NIKHEF, Amsterdam, Netherlands
49
Laboratoire de l’Acce
´
le
´
rateur Line
´
aire (LAL), Universite
´
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
Universita
`
di Milano and Sezione INFN, Milan, Italy
56
Universidade Federal do Rio de Janeiro, Instituto de Fı
´
sica, Rio de Janeiro, RJ, Brazil
57
Universidade de Sa
˜
o Paulo, Instituto de Fı
´
sica, Sa
˜
o Carlos, SP, Brazil
58
Kernfysisch Versneller Instituut, University of Groningen, Groningen, Netherlands
59
Institut de Physique Nucle
´
aire d’Orsay (IPNO), Universite
´
Paris 11, CNRS-IN2P3, Orsay, France
60
RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
61
Michigan Technological University, Houghton, Michigan, USA
62
Pontifı
´
cia Universidade Cato
´
lica, 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’Universita
`
and INFN, Genova, Italy
68
University of Ło
´
dz
´
,Ło
´
dz
´
, Poland
69
Louisiana State University, Baton Rouge, Louisiana, USA
70
Universidade de Sa
˜
o Paulo, Instituto de Fı
´
sica, Sa
˜
o Paulo, SP, Brazil
71
INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy
72
Departamento de Fı
´
sica, FCEyN, Universidad de Buenos Aires y CONICET, Argentina
73
Universidade Estadual de Feira de Santana, Brazil
74
Palacky
´
University, Olomouc, Czech Republic
75
Universita
`
dell’Aquila and INFN, L’Aquila, Italy
76
Universita
¨
t Hamburg, Hamburg, Germany
77
Universidade Federal do ABC, Santo Andre
´
, SP, Brazil
78
Beneme
´
rita Universidad Auto
´
noma de Puebla, Puebla, Mexico
79
Dipartimento di Ingegneria dell’Innovazione dell’Universita
`
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 La
´
seres y Aplicaciones, CITEFA and CONICET, Argentina
83
Instituto de Fı
´
sica Corpuscular, CSIC-Universitat de Vale
`
ncia, 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 Astronomı
´
ayFı
´
sica 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
Universita
`
di Palermo and Sezione INFN, Catania, Italy
95
Konan University, Kobe, Japan
96
Centro de Investigacio
´
n y de Estudios Avanzados del IPN (CINVESTAV), Me
´
xico, D.F., Mexico
(Received 7 December 2009; published 1 March 2010)
We describe the measurement of the depth of maximum, X
max
, of the longitudinal development of air
showers induced by cosmic rays. Almost 4000 events above 10
18
eV observed by the fluorescence
detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are
PRL 104, 091101 (2010)
PHYSICAL REVIEW LETTERS
week ending
5 MARCH 2010
091101-3

selected for the analysis. The average shower maximum was found to evolve with energy at a rate of
ð106
þ35
21
Þ g=cm
2
=decade below 10
18:240:05
eV, and ð24  3Þ g=cm
2
=decade above this energy. The
measured shower-to-shower fluctuations decrease from about 55 to 26 g=cm
2
. 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 com-
position 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 differ-
ent mass composition at Earth. For example, the hardening
of the cosmic ray energy spectrum at energies between
10
18
and 10
19
eV, known as the ‘‘ankle’’, is presumed to be
either a signature of the transition from galactic to extra-
galactic 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 
10
19
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 composi-
tion of cosmic rays cannot be measured directly, but has to
be inferred from observations of extensive air showers. The
atmospheric depth, X
max
, at which the longitudinal devel-
opment 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 hadron-
induced showers and the superposition assumption for
nuclear primaries of mass A, the average depth of the
shower maximum, hX
max
i, at a given energy E is expected
to follow [4]
hX
max
i¼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 energy-
independent parameters  and  in the energy range
considered here, see [6]. Only physics processes not ac-
counted for in currently available interaction models could
lead to a significant energy dependence of these
parameters.
The change of hX
max
i per decade of energy is called
elongation rate [7],
D
10
¼
dhX
max
i
d lgE
 

1 
dhlnAi
d lnE

lnð10Þ; (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, rmsðX
max
Þ, which is expected to de-
crease with the number of primary nucleons A (though not
as fast as 1=
ffiffiffiffi
A
p
[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 X
max
measurements [9,10] focused mainly on
hX
max
i as a function of energy and had only limited statis-
tics above 10
19
eV.
Here we present a measurement of both hX
max
i and
rmsðX
max
Þ using high quality and high statistics data col-
lected with the southern site of the Pierre Auger
Observatory [11]. The observatory is located in the prov-
ince of Mendoza, Argentina and consists of two detectors.
The surface detector (SD) array comprises 1600 water-
Cherenkov detectors arranged on a triangular grid with
1500 m spacing that cover an area of over 3000 km
2
.
The water-Cherenkov detectors are sensitive to the air
shower components at ground level. The fluorescence de-
tector (FD) consists of 24 optical telescopes overlooking
the array, which can observe the longitudinal shower de-
velopment by detecting the fluorescence and Cherenkov
light produced by charged particles along the shower tra-
jectory 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 func-
tion of atmospheric depth. X
max
is determined by fitting the
reconstructed longitudinal profile with a Gaisser-Hillas
function [17].
PRL 104, 091101 (2010)
PHYSICAL REVIEW LETTERS
week ending
5 MARCH 2010
091101-4

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