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U p p e r L i m i t o n t h e C o s m i c - R a y P h o t o n F l u x

A b o v e 1 0 19 e V U s i n g t h e S u r f a c e D e t e c t o r o f t h e

P i e r r e A u g e r O b s e r v a t o r y

The Pierre Auger Collaboration: J . A b r a h a m 14, P. A b re u 69,

M . A g lie t ta 55, C . A g u ir re 17, D . A lla rd 33, I. A lle k o tte 7, J . A lle n 89, P. A lliso n 91, J . A lv a re z -M u n iz 76, M . A m b ro s io 58,

L. Anchordoqui103,90, S. A ndringa69, A. Anzalone54, C. A ram o58, S. Argiro52, K. Arisaka94, E. A rm engaud33, F. Arneodo56,

73 39 5 6992 35 95 13 43

10 19 94 2583 91 33 100

37 92 102 3642 48 5 40

35 35 73 86, 46, 57

C. Bleve79, H. Bliimer42,38, M. Bohacova31, C. Bonifazi35,19, R. Bonino55, M. B oratav35, J. Brack83,96, P. Brogueira69,

84 43 75 8133 42 98 47

40 51 21 55 54 48 95 52

36 55 23 89, 8688 78 16 2

R. Conceigao69, B. Connolly100, F. C ontreras12, J. Coppens63,65,34 61 92 81

71 92 95 4034 38 16

23 47 6315 23

J.R .T . de Mello Neto95,28, I. De M itri48, V. de Souza42,74 32 49 50

41 50 88 23

Preprint submitted to Elsevier Science 2 February 2008

J.C . D ’Olivo62, D. Dornic32, A. Dorofeev87, J.C . dos Anjos19, M.T. Dova10, D. D ’Urso49, I. D utan40, M.A. DuVernois97,98,

R. Engel38, L. Epele10, M. Erdm ann41, G O .E sco b ar23,A. Etchegoyen3, P. Facal San Luis76, H. Falcke63,66, G. Farrar89,

23 86 81 71 88

A. Filevich2, A. Filipcic70, I. Fleck43, R. Fonte51,C.E. Fracchiolla20, W. Fulgione55, B .G a rc ía 14,

75 73 34

H. Geenen37, G. Gelmini94, H. Gemmeke39, P.L. G hia32,55,68 86 100 6

10 6 7469 29 42

J.G . Gonzalez87, M. González60, D. G òra42,67, A. Gorgi55,21 47 56 10

8 49 24 74100 33 76 6

S. H arm sm a64, J.L. H artón32,83, A. Haungs38, T. H auschildt55,94 41 74 38

86 16 67 6363 71 31 38

71 46 51 95 5186 37 31 34

42 23 88 3839 38 83 7936 2 39 37

39 94 54 3328 36 86 94

27 35 4132 59 76

75 60 5446 55 48 10

31 86 10 4261 48 60

59 38 87, 93100 50 52 86

2

T. M cCauley90, M. McEwen74,87, R.R. McNeil87, M.C. M edina3, G. M edina-Tanco62, A. Meli40, D. Melo2, E. M enichetti52,

A. Menschikov39, Chr. M eurer38, R. M eyhandan64,M .I. M ic h e le t# , G. M iele4^ W. M ille r100, S. M o lle rac h 6,M. M onasor73,74, D. Monnier Ragaigne34, F. M ontanet36,

62 55 10 91

M . M o s ta fa 101, M .A . M u lle r23, R . M u ssa 52, G . N a v a rra 55,75 75 31 62

86 79, 76 10437 88 30 31

38 94 33, 9576 73 50

42 14 74 2331 1 76 33 5672 79 90 95 36

31 67 60 26 5346 50 83 104

104 104 11 838 69 72 51

49 2 5 50 311 37 74 90

33 19 31 51 3736 46 92 59

76 74 5112 76 73, 74

73 38 35 336 11 46 59

50 62 12 69

E.M. Santos35, 19, F. Sarazin82, S. Sarkar77, R. Sato12,37 38 39 95

42 64 31 3810 51 54 33

M. Settim o48, R.C. Shellard19,20, I. Sidelnik3, B.B. Siffert28,33 2 68

31 16 79 99

3

P. Sokolsky101, P. Sommers92, J. Sorokin16, H. Spinka80,86, R. Squartini12, E. Strazzeri50, A. S tu tz36, F. Suarez55,

T. Suomijarvi32, A.D. Supanitsky62, M.S. Sutherland91,90 68 23 11

A. Tam burro42, O. Ta§cau37, R. Tcaciuc43, D. Thom as101, R. T icona18, J. Tiffenberg8, C. T im m erm ans65,63, W. Tkaczyk68,

23 69 52 5954 31 94 33

D. T sc h e rn ia k lio v sk i39, M. Tueros9, V. T u n n ic liffe78, R. Ulrich38, M . U n g e r38, M . U rb a n 34, J .F . Valdés G a lic ia 62, I. Valiño76,

49 64 3276 71 10 18

T. Venters95,33, V. Verzi50, M. Videla15, L. Villaseñor61,71 86 10 4

78 83 79 10268 82 67 67

79 16 34 295 101 76 71

70 35 60 43

1 Centro de Investigaciones en Láseres y Aplicaciones, CITEFA and CONICET,Argentina

2 Centro Atómico Constituyentes, CNEA, Buenos Aires, Argentina3 Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica and

CONICET, Argentina4 Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica and

UTN-FRBA, Argentina5 Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, San Carlos

de Bariloche, Argentina6 Departamento de Física, Centro Atómico Bariloche, Comisión Nacional de

Energía Atómica and CONICET, Argentina7 Centro Atómico Bariloche, Comision Nacional de Energía Atómica and Instituto

Balseiro (CNEA-UNC), San Carlos de Bariloche, Argentina 8 Departamento de Física, FCEyN, Universidad de Buenos Aires y CONICET,

Argentina9 Departamento de Física, Universidad Nacional de La Plata and Fundación

Universidad Tecnológica Nacional, Argentina10 IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina

11

Argentina12

4

13 Pierre Auger Southern Observatory and Comisión National de Energia Atòmica, Malargüe, Argentina

14 Universidad Tecnològica National, FR-Mendoza, Argentina 15 Universidad Tecnològica National, FR-Mendoza and Fundación Universidad

Tecnològica National, Argentina16 University of Adelaide, Adelaide, S.A., Australia17 Universidad Catolica de Bolivia, La Paz, Bolivia

18 Universidad Mayor de San Andrés, Bolivia19 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil

20 Pontificia Universidade Católica, Rio de Janeiro, RJ, Brazil 21 Universidade de Sao Paulo, Inst. de Fisica, Sao Paulo, SP, Brazil23

2425

2627

2829

30

Republic31

Czech Republic32

France33

Paris, France34

Orsay, France35

7 and IN2P3/CNRS, Paris Cedex 05, France36

Université Grenoble 1 et INPG, Grenoble, France37

3839

Elektronik, Germany40

4142

Karlsruhe, Germany43

464748

4950

51

5

52 Università di Torino and Sezione INFN, Torino, Italy53 Università del Salento and Sezione INFN, Lecce, Italy

54 Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo,Italy

55

Sezione INFN, Torino, Italy56 INFN, Laboratori Nazionali del Gran Sasso, Assergi (L ’Aquila), Italy

57 Osservatorio Astrofisico di Arcetri, Florence, Italy58 Sezione INFN di Napoli, Napoli, Italy

59 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico60 Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV),

México, D.F., Mexico61 Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico

6263

64

Netherlands6566

6768

6970

7172

737475

7677

United Kingdom78

Kingdom,79

8081

8283

8486

8788

899091

9293

6

94 University of California, Los Angeles, CA, USA 95 University of Chicago, Enrico Fermi Institute, Chicago, IL, USA

96 University of Colorado, Boulder, CO, USA 97 University of Hawaii, Honolulu, HI, USA

98 University of Minnesota, Minneapolis, MN, USA99

100 University of New Mexico, Albuquerque, NM, USA 100 University of Pennsylvania, Philadelphia, PA, USA

101 University of Utah, Salt Lake City, UT, USA102 University of Wisconsin, Madison, WI, USA

103 University of Wisconsin, Milwaukee, WI, USA104

A b stra c t

A method is developed to search for air showers initiated by photons using data recorded by the surface detector of the Auger Observatory. The approach is based on observables sensitive to the longitudinal shower development, the signal risetime and the curvature of the shower front. Applying this method to the data, upper limits on the flux of photons of 3.8 x 10-3 , 2.5 x 10-3 , and 2.2 x 10-3 km-2 sr-1 vr-1 above 1019 eV, 2 x 1019 eV, and 4 x 1019 eV are derived, with corresponding limits on the fraction of photons being 2.0%, 5.1%, and 31% (all limits at 95% c.l.). These photon limits disfavor certain exotic models of sources of cosmic rays. The results also show that the approach adopted by the Auger Observatory to calibrate the shower energy is not strongly biased by a contamination from photons.

1 Introduction

The search for photons in the u ltra-high energy (UHE) cosmic-ray flux has been stim ulated by the observation of cosmic rays w ith energies exceeding E gzk ~ 6 x 1 019 eV [1,2,3,4,5,6], If these particles are due to eosmologieally d istan t sources, the flux spectrum is expected to steepen above th is energy. In- triguinglv, a flux spectrum w ith no apparent steepening above E GZK has been reported by the AG AS A C ollaboration [7]. To account for th is observation and to circum vent the theoretical challenge of explaining particle acceleration to such energies, models involving new physics have been proposed in which the cosmic rays are created a t the observed energies a t relatively close distances from the E arth . These “top-dow n” models [8,9] may involve super heavy dark m a tte r (SHDM) [10,11,12], topological defects [13], or neutrino interactions w ith the relic neutrino background (Z-bursts) [14]. A com mon feature of these models is the prediction of a substan tial photon flux a t highest energies.

7

The Auger C ollaboration has recently reported a m easurem ent of the eosmie- rav spectrum from the Auger South site showing a flux suppression above E gzk [15], The Auger m ethod is based on a large surface array to collect the required sta tistics and a fluorescence detector to calibrate the energy scale. Us­ing th is “hybrid” approach, the energy reconstruction is largely independent of hadronic in teraction param eters and, in case of nuclear prim aries, of the pri­m ary mass com position. However, as explained la ter, the energy assignm ent from surface arrays can be substan tially altered in the case of prim ary pho­tons, This would affect the reconstructed p rim ary spectrum if a non-negligible num ber of the highest-energv events, where d a ta from the fluorescence tele­scopes are sparse due to the ir ~10% duty cylee, was actually due to photons (see also [16]), I t is worthwhile to note th a t the acceptance of fluorescence detectors (as also applied in the HiRes experim ent [5]) can be altered in the case of photon prim aries [17,18,19],

UHE photons can also act as tracers of the GZK (G reisen-Zatsepin-K uzm in) process [20] of resonant photopion production of nucleons off the cosmic mi­crowave background. The corresponding photon fluxes are sensitive to source features (type of prim ary, injection spectrum , distance to sources ,,,) and to propagation param eters (extragalactic radio backgrounds and m agnetic fields) [9,21,22,23,24],

Thus, the search for prim ary photons rem ains an im portan t subject for various reasons [25], particu larly

• to set significant lim its to the possible contribu tion of top-dow n mechanismsto the prim ary eosmie-rav flux;

•and propagation models;

the energy estim ate in the surface array detector would be altered;

gravity effects in the electrom agnetic sector [26],

Showers in itia ted by UHE photons develop differently from showers induced by nuclear prim aries. Particularly , observables related to the developm ent stage or “age” of a shower (such as the dep th of shower m axim um X max) and to the content of shower muons provide good sensitivity to identify prim ary pho­tons, Pho ton showers are expected to develop deeper in the atm osphere (larger X max). This is connected to the sm aller m ultiplicity in electrom agnetic in ter­actions com pared to hadronic ones, such th a t a larger num ber of interactions is required to degrade the energy to the critical energy where the cascading process stops. Additionally, the LPM effect [27] results in a suppression of the pair production and brem sstrahlung cross-sections. Pho ton showers also contain fewer secondary muons, since photoproduction and direct muon pair

8

production are expected to play only a sub-dom inant role.

Searches for photons were previously conducted based on surface arrays [28,29,30,31,32], and lim its to the fraction of photons were reported (see [25] for a review). The derivation of lim its to the photon fraction using surface array d a ta alone is an experim ental and conceptual challenge (see also Section 2,3), Firstly, for conclusions on the fraction, the energy scales for photon and nuclear prim aries are needed. These energy scales may differ from each o ther for surface arrays, and the difference between the scales may depend in a non-trivial way on prim ary param eters such as the shower zenith angle. Secondly, the energy re­construction of nuclear prim aries suffers from substan tia l uncertain ties due to our lim ited knowledge of high-energy hadron dynam ics.

B oth issues can be resolved using the fluorescence technique, which is near- calorim etric and largely independent of sim ulating hadron interactions, A cor­responding approach has been developed and applied recently to ob ta in a first bound on the fraction of photons from d a ta taken a t the Auger Observa­tory [19],

In th is work, using the larger num ber of events recorded by the surface array, we derive for the first tim e a direct lim it to the flux of photons by searching for photon candidates and relating the ir num ber to the well-known exposure of the surface array. This avoids the need of sim ulating events in itita ted by nuclear prim aries; only the photon energy scale is needed which can be sim ulated w ith much higher confidence. Two observables of the surface detectors are chosen which have significantly different behavior for nuclear prim aries when com pared to photons: the risetim e of the recorded shower signal and the radius of curvature of the shower front.

We also derive a lim it to the fraction of photons. W hile the challenge of using two energy scales rem ains for th is p a rt of the analysis, hadron sim ulations can still be avoided by using the hybrid calibration [15] to reconstruct the energies of the observed events.

The plan of the paper is as follows. In Section 2, the observables used in the analysis and the ir relationship w ith the com position of cosmic rays are explained. In Section 3, the sim ulation of UHE photons is considered. The m ethod developed to distinguish events which are photon candidates using observables of the surface detector is detailed in Section 4, In Section 5, the results are presented. The conclusions are given in Section 6 ,

9

2 Observables

The analysis in th is paper is based on d a ta taken during 21,400 hours of operation of the surface detector recorded in the period 1 January 2004 to 31 Decem ber 2006, The surface detector, when com pleted, will have 1600 w ater Cherenkov detectors spaced 1,5 km ap art and covering 3000 km 2 [33,34], Each w ater Cherenkov detector, or s ta tion , is a cylinder 1,2 m in height and 3,6 m in diam eter. Each detector is lined w ith a reflective container th a t holds 12 tonnes of purified w ater and is fitted w ith th ree nine-inch photom ultip lier tubes (PMTs) looking down into the water.

W hen a relativ istie particle passes through a s ta tion , Cherenkov radiation is em itted . The rad ia ted photons then propagate through the w ater, being reflected a t the sta tion walls, and are either eventually absorbed or detected by a PM T, The signals from the PM Ts are digitised by a flash analog to d igital converter (FADC) which samples the signal every 25 ns. These digitised signals are then tran sm itted to a central d a ta acquisition system where event triggers are built. Each event, then, has a detailed tim e profile Si(ri}t) of the energy deposited in each sta tion i a t distance r in the shower plane. The function s(r, t) depends in a complex wav bo th on the param eters of the prim ary particle (energy, type, direction) and on the detector response to different secondary particles (particu larly the electrom agnetic and muonic shower com ponents).

In th is work, we ex tract two relatively simple bu t robust observables from these da ta , noting th a t the w ealth of inform ation contained in the tim e profiles can fu rther be exploited in fu ture work. The observables, the radius of curvature of the shower front and the risetim e a t 1000 m core distance, were found to provide good discrim ination between photon and nuclear prim aries (see e.g. also Ref, [35]), In addition to the quan tita tive studies of these observables by m eans of the sim ulation-reconstruction chain, we will also sketch (in a simplified way) why these observables are indeed expected to differ between nuclear and photon prim aries.

2.1 Radius o f Curvature

Due to geom etrical reasons, the arrival of the first particles a t la teral distance r from the axis is expected to be delayed w ith respect to an (im aginary) p lanar shower front (see also Fig, 1, left p lot). For a particle th a t is due to an earlier in teraction a t height H along the shower axis and observed a t r , the delay

10

from the longer p a th length can be approxim ated as

i _______ r 2t = - ( \J H 2 + r 2 — H ) oc — (r <C H ).

c H (1)

The delay increases (for r ^ H about quadratically) w ith r, Im portan tly , the delay decreases w ith increasing height H , Air showers w ith the first ground particles coming from relatively large heights will have sm aller delays t a t fixed

rsm aller heights. C om pared to p rim ary photons, showers from nuclear prim aries develop higher in the atm osphere (sm aller X max), Additionally, shower muons (much more abundan t in showers from nuclear prim aries) can reach the ground from still higher altitudes fu rther reducing the tim e delay. Thus, for nuclear prim aries sm aller delays are expected com pared to photon prim aries.

We make use of th is relation by fitting a shower front (abstract surface w ith convex curvature defined by the fastest shower particles) to the m easured trigger tim es tj(rj) of the first particles registered a t distances r*. In the present study, the shape of the shower front is approxim ated using a spherical model (in accord w ith Eq, (1)), and the radius of curvature R of the shower front is obtained by m inim izing x 2 in the function

where t i is the trigger time for sta tion i as defined in [36], t 0 is the tim e of the shower in the center of curvature, a is the un it vector along the shower axis, x i is the location of the sta tion on the ground relative to the shower core, and at is the uncertain ty in the shower arrival tim e [37], In the determ ination of t irelated to the actual shower,

2.2 R isetim e

Also the spread in tim e of the signal Sj(rj, t) registered a t distance r i; which corresponds to the thickness of the local shower disk, can be ex tracted. Using Eq, (1), the difference of arrival tim es of particles originating from a height interval [H i, H i — A H ] follows as

(2)

A t(H i, A H ) « r 21 1 \ r 2A H

°Cr VHi — A H h J H i (H i — A H )

< A t(H 2, A H ) for H < H i. (3)

11

Fig. 1. Illustration of geometrical effects on radius of curvature and risetime of the shower front. (Left) With respect to an imaginary planar shower front, particles arrive more delayed at distance r when originating from a smaller height H 2 < H i. Correspondingly, the radius of curvature of the actual shower front is smaller in case of the deep developing photon primaries. (Right) The spread of arrival times of particles produced over a pathlength A H and arriving at distance r increases for a smaller production height H 2 < H i . Correspondingly, the risetime of the shower is increased in case of the deep developing photon primaries.

The spread of arrival tim es of these particles a t fixed core distance increases for sm aller production heights (see also Fig. 1, right plot). Accordingly, a larger spread is expected in case of the deep developing photon prim aries (larger X max), We note th a t in general, the situa tion is more complex. The tim e spread may depend on details of the previous shower development, par­ticu larly also on the com petition between the signals from the electrom agnetic and muonic shower com ponents which will be com m ented on below. Still, geo­m etrical effects are essential in the relation between tim e spread and prim ary com position.

In th is study, we use the risetim e t 1/ 2 (1000) of the shower signal reconstructed for 1 0 0 0 m distance and located along the line given by the projection of the shower axis onto the ground. F irst, the risetim e tm/e2as(ri ) of a single sta tion is defined as the tim e it takes to increase from 10% to 50% of the to ta l sig­nal deposited in th a t station . According to Eq. (3), for non-vertical showers a (m oderate) dependence of tm/<2as(ri ) on the in ternal azim uth angle of the stations w ithin the shower plane is expected. This is because the height H m easured along the shower axis is larger for those stations on the exterior side

12

of the shower com pared to those on the interior side of the shower. To account for this, the observed tm/2as(ri) are corrected depending on the in ternal azim uth angle Z of th a t station:

t1/2(ri) = tm/e2as (ri) - g ■ cos Z (4)

g = -6 6 .6 1 + 95.13 ■ sec 9 - 30.73 ■ sec2 9 + [0.001993 ■ sec 9 -0 .001259 ■ sec2 9 + 0.0002546 ■ sec3 9 - 0.0009721] ■ r 2

where the param eter g depends on distance r and prim ary zenith angle 9Z

projection of the shower axis on the ground and the line connecting the shower im pact point and the station.

It is also expected from Eq, (3) th a t the values t i °r2 (r i) depend on the distance r i of the stations. We obtain the final risetim e t 1/2 (1000) of the shower bv perform ing a fit to t i°r2 (r i) using the function

t 1/ 2 (r) = (40 + a r + br2) ns . (5)

The param eters a and b are determ ined for each event by fitting the sta tion d a ta (typical values are 50 ns km -1 and W0 ns km - 2 respectively). The func-

rin the w ater Cherenkov detectors.

W hile geom etrical effects connected to the different shower developm ents from nuclear and photon prim aries are a m ain reason for the risetim e difference (larger t 1/2 ( 1 0 0 0 ) in photon showers), again th is sensitivity to com position is fu rther strengthened by shower mouns which are more abundan t in the case of nuclear prim aries and can dom inate the registered signal a t larger zenith angles. As muons tend to arrive w ithin a shorter tim e window com pared to the electrom agnetic com ponent which suffers from m ultiple scattering, this fu rther reduces the risetim e t 1/2 ( 1 0 0 0 ) for nuclear prim aries,

2.3 Energy

As an energy estim ator, the tim e-in tegrated energy deposit S (1000) a t 1000 m core distance is used [38], However, for the same in itia l energy and direction the average S (1 0 0 0 ) from prim ary photons can be a factor > 2 below th a t from nuclear prim aries [39,40], Reasons are the (typically factor ~ 4 ) sm aller num ber of muons and, due to the la te r developm ent, the steeper ground la teral d istribu tion in prim ary photon showers. For a lim it to the fraction of prim ary photons, the energy scales (transform ation from S ( 1 0 0 0 ) to prim ary energy)

13

for b o th photon and nuclear prim aries are required, while the determ ination of a lim it to the flux can rely on the photon energy scale alone.

The energy scale for nuclear prim aries is based on the fluorescence technique by using events th a t are detected w ith b o th the surface detector and the fluo­rescence telescopes [41], The energy scale for photon prim aries (which induce alm ost purely electrom agnetic cascades) is taken from sim ulations. Thus, bo th approaches are largely independent from assum ptions abou t hadron interac­tions a t high energy,

S(1000)energy scale results in a (relatively poor) resolution of abou t 40%, To improve this, a unique energy conversion for photons is applied th a t is described in detail in Ref, [40], It is based on the universality of shower developm ent [42], i.e. the electrom agnetic p a rt of the shower is expected to develop in a well- predictable m anner for depths exceeding X max, In brief, for given values of S (1000) and X max, the prim ary energy is estim ated by

= L4(1 + + ( A ^ m oE.y y 1000 n y 340 ; J 1 ;

w ith A X — X ground X max j

S(1000)the photon energy is in EeV, and A X is in g cm -2 . Since X max is not directly m easured by the surface detector alone, an iterative approach using Eq, (6) is taken to estim ate the energy. A fter an initial guess of the photon energy using S (1000) alone, the tvpical X max of the photon showers a t th is energy is taken

X maxenergy is obtained using Eq, (6), and the procedure is repeated. The energy estim ate is found stab le after few iterations and an energy resolution of 25% is achieved [40], We use th is im proved estim ation of the photon energy, bu t note th a t the m ain conclusions rem ain valid also when using a direct energy estim ation.

3 M onte Carlo Sim ulations

The QED processes of LPM effect [27] and geom agnetic cascading ([43,35] and references therein) need to be considered for photon showers a t highest energy. As m entioned before, the LPM effect leads to a suppression of th e pair produc­tion and brem sstrahlung cross-sections and, thus, additionally increases the separation of photon and nuclear prim aries in term s of X max (for a review of the

14

In case of geom agnetic cascading of UHE photons, the in itia l conversion of the UHE photon into an electron-positron pair can induce a “preshower” (mostly synchrotron photons plus electron-positron pair(s)) outside the atm osphere. The subsequent air showers from such “converted” photons develop higher in

X maxphotons do. As geom agnetic cascading becomes im portan t a t energies above ~50 EeV at the southern site of the Auger Observatory, th is process is of m inor relevance for the bulk of d a ta used in th is analysis.

The shower sim ulations were generated w ith the Aires sim ulation package (v2,8), which includes the LPM effect and geom agnetic cascading [45], QGS- JE T 01 [46] was used as the hadronic in teraction model. The sim ulation of the w ater Cherenkov detectors uses the CHANT I [47] sim ulation package along w ith specific code th a t handles PM T response and d a ta acquisition electronics. The result is th a t the ou tp u t of a sim ulated event is in a form at th a t is identical to the d a ta form at recorded w ith the Auger Observatory, The shower reconstruction procedure used is the sam e for real events as it is for sim ulated events to avoid system atic differences a t the reconstruction stage.

1

4 M ethod

In brief, the lim it to the photon flux is ob tained as follows. Selection cuts are applied to the d a ta (and sim ulations) to ensure events of good reconstruction

S(1000)showers above a m inim um prim ary energy are selected. This d a ta set is then searched for photon candidates using t 1/ 2 (1000) and R (see Section 2 for defini­tions), Sim ulations assum ing photons are used to determ ine the corresponding selection efficiencies. From the num ber of photon candidates, the efficiencies w ith respect to photons, and the experim ental exposure (obtained from the geom etrical acceptance known from detector m onitoring), the upper lim it to the photon flux is derived.

The criteria to select events of good quality are:

• the sta tion w ith the largest signal is surrounded by 6 active stations;• >

> > equivalent muons) [36];

1a significantly larger X max than nuclear primaries (differences >150 g cm2 above 1019 eV) and a smaller number of muons.

15

0.5 0.6 0.7 0.8 0.9 1.0Cos(B)

Fig. 2. Photon detection and reconstruction efficiency (right hand scale) as a function of the energy (in EeV) and zenith angle of the primary photon. The analysis is restricted to a minimum energy of 10 EeV and zenith angles greater than 30° and less than 60° (0.866 > cos6 > 0.5).

• reduced x 2 < 10 (x 2 from Eq, (2)).

The first cu t restric ts the analysis to well-contained events, elim inating in particu lar events near the border of the array. It affects the geom etrical ac­ceptance only. The m ultiplicity criterion in the second cut is im portan t also to ensure a good reconstruction of t 1/ 2 (1000) and R. As the m ultiplicity isrelated to prim ary energy, th is cu t also affects the energy-dependent accep-

x 2

distribu tion when reconstructing R , removing ~4% of data . As noted before, the assum ption of a spherical model used in Eq. (2) is a sim plification and, thus, not expected to provide a perfect description of the com plex features of the shower front. This cu t restric ts the analysis to events where a single value

Rno bias to photons is introduced th is way.

As can be seen from Fig. 2, the resulting photon efficiency drops to small values below ~ 10 EeV. At higher energy, near-vertical photons can also fail the sta tion m ultiplicity cu t due to the ir deep development. Therefore, the analysis is restric ted to

• >• prim ary zenith angles of 3 0 -6 0 °,

16

Fig. 3. Parameterization of the mean behavior of R and t i / 2 for 20 EeV primary photons as a function of the zenith angle using QGS.JET 01 [46] or SIBYLL 2.1 [49]. The mis values are indicated for the case of QGS.JET 01. An increase (a decrease) of R (of t 1/ 2) with zenith angle is qualitatively expected from Eqs. (1) and (3) due to the generally longer path lengths to ground in case of larger inclination. Real events of 19 21 EeV (photon energy scale) are added. The significant deviation of the observed values from those expected for primary photons is visible.

Events w ith zenith angles below 60° are selected here since inclined show­ers require dedicated algorithm s for an optim um reconstruction |50| (this cut m ight be relaxed in the future).

The search for photon candidates makes use of i 1/2(1000) and R and consists of the following steps. Firstly, the deviation A x of the observable x (with x = ¿a/2 or R referring to risetim e or radius of curvature, respectively) from the m ean value X7 predicted for photons is derived in units of the spread a x,7

x

A = x - ^7(5(1000), 0)T aT,7(S(lOOO),0) '

where XY(S (1000), 0) and a x,7 (S (1000), 0) are param eterized from sim ulations using prim ary photons. In Fig. 3, exam ples are shown for these param eteriza- tions of the observables along w ith d istribu tions of real events.

Secondly, we combine the inform ation contained in the quantities A tl/2 and A r by perform ing a principal com ponent analysis [51], leaving a more sophisti­cated sta tis tica l analysis for the future. To determ ine the principal com ponent (defined as the axis w ith the largest variance), 5% of the real events are used together w ith results from photon sim ulations, see Fig. 4. For the sim ulations, a power law spectrum of index -2.0 has been assum ed (see below for other indices). The rem aining 95% of the d a ta are then projected onto the principal axis along w ith the sim ulated photons.

This procedure allows the a priori definition of a simple cut in the projected

17

Fig. 4. The deviation from a photon prediction for 5% of the data (closed squares) and simulated photon events (crosses). The solid grey line is the principal component axis identified using the limited set of real showers while the dashed line is the axis perpendicular to the principal component. The minimum energy is 10 EeV (E7 > 10 EeV).

d istribu tion to finally ob ta in photon cand idate events. The cut was chosen a t the m ean of the d istribu tion for photons, such th a t the efficiency of this cut is ƒ = 0.5 by construction. Any real event falling above th is cut will be considered a photon candidate. We note th a t such photon candidates, if occuring, can not yet be considered as being photons, as they actually m ight be due to background events from nuclear prim aries. A presence of background events would result in weaker upper lim its (larger num erical values) in the analysis approach adopted here.

Finally, an upper lim it on the num ber of photons N C L at confidence level CL is calculated from the num ber of photon candidate events above a m inim um energy, E min. The upper lim it on the flux or fraction of photons above a given energy is based on N C L along w ith the in tegrated efficiency e of accepting photons, the photon selection cut efficiency (ƒ = 0.5), and either the exposure A of the detector for the flux limit:

Ar °L(E y > E min) x ) x

E > = ------------------ o . 9 M • <8 >

18

or the num ber of non-photon cand idate events N non-Y in the d a ta set for the fraction limit:

, , A/"c l (E 7 > E min) x } x j T c l(E > = ; 7 ------- * • . (9)

N Y(E Y > E min) + N non-7 (E non- 7 > E min)

In Eq, (8), the factor 0,95 is from the fact th a t only 95% of the d a ta are used to determ ine the num ber of photon cand idate events. The energy is labeled as either the energy according to the photon energy reconstruction, E 7, or (required in Eq, (9)) the energy according to the non-photon energy recon­struction , E non-7,

Experim entally, the lim it $ CL to the flux is more robust th an the lim it F CL to the fraction due to the different denom inators of Eqs, (8) and (9), For F CL, two energy scales are required; also, w ith increasing energy, the s ta tis tica l uncertainty of the quan tity (NY + N non-Y) becomes large. For $ CL, in contrast, the apertu re is known to good (~3% ) accuracy.

Though the present work does not aim at ex tracting a com position of nuclear prim aries, it is interesting to check w hether the principal com ponent axis found from real d a ta and the separation along it reflects w hat would be expected if the bulk of the real d a ta is due to nuclear prim aries. In Fig, 5, the same sim ulated photon events are used as in Fig, 4 bu t the 5% of real d a ta are replaced w ith a set of ~750 M onte Carlo pro ton and iron showers w ith an energy of 10 EeV, The separation observed in real d a ta is bo th in the same direction and of a sim ilar m agnitude as th a t expected from sim ulated nuclear prim aries.

5 R e s u l t s

The d a ta from 2004-2006 are analysed as described in the preceding section. The in tegrated apertu re of the O bservatory is 3130 km 2 sr vr for the angular coverage regarded in th is analysis. Above 10, 20, and 40 EeV, for the energy scale of photons (in brackets for nuclear prim aries), the d a ta set consists of 2761 (570), 1329 (145), and 372 (21) events. The m easured values of t i / 2(1000) and R are used to determ ine the projection on the principal axis, A sca tte r plo t of th is quan tity vs, the p rim ary energy is shown in Fig, 6, while in Fig, 7 the corresponding d istribu tions are p lo tted for the th ree threshold energies. No event passes the photon cand idate cut. The upper lim its on the photon flux above 10, 20, and 40 EeV are then 3.8 x 10-3 , 2.5 x 10-3 , and 2.2 x 10-3 km -2 sr-1 v r-1 (at 95% CL), The lim its on the photon fraction are 2,0%, 5,1%, and 31% (at 95% CL) above 10, 20, and 40 EeV, In Tab, 1, all relevant quantities (num ber of events, efficiencies, resulting lim its) are sum m arized.

19

Fig. 5. The black crosses are simulated photon showers while the squares are a mixture of Monte Carlo proton and iron with an energy of 10 EeV. For comparison, the lines shown in Fig. 4 (principal component axes) are added. The distribution of simulated nuclear primaries is similar to the distribution of real data seen in Fig. 4.

E ■-L/min N (E 7 > E min) v 7 ^0.95 Vnon—7 t $ 0 95 •̂ 0.95

10 2761 0 3.0 570 0.53 3.8 X 10“ 3 2.0%.

20 1329 0 3.0 145 0.81 2.5 X 10“ 3 5.1%

40 372 0 3.0 21 0.92 2.2 X 10“ 3 31%Table 1Results of the analysis searching for photon candidate events. The fraction and flux limits are integral limits above E min (EeV), e is the efficiency of detection and reconstruction, $ 0.95 is in units of km-2 sr-1 yr-1 , and all results are 95% confidence level.

From Fig. 6 it can also be seen th a t the separation of d a ta and photon pri­m aries increases w ith energy. In particu la r a t highest energies above E GZK for the photon energy scale, there is no indication for pho ton-in itia ted events. Thus, the absence of photons, w ithin the improved lim its placed in th is work, shows th a t the m ethod applied by the Auger O bservatory to calibrate the shower energy is not strongly biased by a photon “contam ination”.

We studied po ten tial sources of system atic effects in the analysis. To determ ine the efficiency to photons and to establish the photon candidate cut, a prim ary

20

Log(Energy/EeV)

Fig. 6. The deviation of data (black crosses) and photons (open red circles) from the principal component as a function of the primary energy (photon energy scale). Data lying above the dashed line, which indicates the mean of the distribution for photons, are taken as photon candidates. No event meets this requirement.

photon spectrum of power law index -2.0 has been used in the sim ulations, m otivated by predictions from top-dow n models in (e.g. in Ref. |10|), The effect of changing the power law index to -1.7, -2.5, and -3.0 has been investigated. The num ber of events which are photon candidates is unchanged (along w ith the num ber of non-photon cand idate events), bu t the correction for the photon efficiency changes. Specifically, for a steeper inpu t spectrum (increased fraction of lower-energy photons), the efficiency decreases. The sum m ary of the results can be seen in Table 2. For 10 EeV threshold energy, lim its change from (3 .8 ^ 5 .5 )x 1 0 -3 km -2 s r-1 v r-1 for the flux and from (2 .0 ^ 2 .9 )% for the fraction. The differences get sm aller w ith increased threshold energy.

The photonuclear cross-section used in the sim ulation is based on the Particle D ata G roup (PD G ) ex trapo lation 1521. For an increased cross-section, more energy would be transfered to the hadron (and muon) com ponent which could dim inish the separation power between d a ta and prim ary photons |53|, From un ita rity constraints, the cross-section is not expected to exceed the PD G ex­trapo la tion by more th a n ~75% at 10 EeV [54]; a t 1015 eV, where the difference in cross-section would have a greater im pact on the shower development, the m axim um difference is ~20% , From sim ulations w ith modified cross-sections it was verified th a t th is leads to a negligible variation of the average values of

21

+ttl I

1 1 1

t t {

* r+* <̂b,<*nL.n.<y?010-i

<> +

MC Photons

Data

I

tt

+ *;

I0 >

I

MC Photons

Data

-1 0 -8 -6 -4 -2 0 2 4 6 8 10 -1 0 -8 -6 -4 -2 0 2 4 6 8 10

1 1

MC Photons

Data

it vI it-4 lo-fofax-j I

-1 0 -8 -6 -4 -2 0 2 4 6 8 10

1

Fig. 7. Distribution of real events (closed squares) along with simulated photon events (open circles) for the projection on the principal component axis. The photon candidate cut is set at the mean of the distribution for photons and is shown as the dotted line. The plots are made requiring a minimum energy (according to the photon energy converter) of 10 EeV (top-left), 20 EcV (top-right), and 40 EcV (bottom). Distributions are normalised to unity at maximum.

the discrim inating variables used in the current analysis.

The sim ulations have been perform ed w ith AIRES using the Q G SJE T had- ronic in teraction model. As a cross-check, calculations w ith CORSIKA 1551 / Q G SJE T and AIRES / SIBYLL were conducted, bo th of which show reason­able agreem ent to the AIRES / Q G SJE T case. As the cascade in itia ted by p rim ary photons has an alm ost pure electrom agnetic nature , indeed no sig­nificant effect is expected when changing to another in teraction model. This m inor dependence of the results on the details of hadron interactions, which are largely uncertain a t high energy, is an im portan t advantage of searches for p rim ary photons.

The new lim its are com pared to previous results and to theoretical predictions

22

E ■-^min 10 20 40 10 20 40 10 20 40

a Efficiency (e) Flux (x10 - 3) Fraction [%]

1.7 0.60 0.83 0.93 3.3 2.4 2.2 1.8 5.0 31

2.0 0.53 0.81 0.92 3.8 2.5 2.2 2.0 5.1 31

2.5 0.43 0.76 0.91 4.7 2.6 2.2 2.5 5.4 31

3.0 0.36 0.71 0.90 5.5 2.8 2.2 2.9 5.9 32Table 2Results when changing the exponent (a) in the power law of the simulated spectrum.The default value is 2.0. The efficiency of detection and reconstruction is on the left,the resulting limit on the fraction of photons is on the right, and the limit on the

-2 -1 -1

in Fig. 8 for the photon flux and in Fig. 9 for the photon fraction. We placed the first direct lim it to the flux of UHE photons (an earlier bound from AGASA, about an order of m agnitude weaker th a n the current bounds, was derived indirectly via a lim it to the fraction and the flux spectrum [29]). In term s of

10-2

while previous bounds were a t the 10-1 level.

A discovery of a substan tial photon flux could have been in terpreted as a signa­tu re of top-dow n models. In tu rn , the experim ental lim its now pu t strong con­stra in ts on these models. For instance, certain SHDM or TD models discussed in the lite ra tu re (SHDM and TD from Ref. [21] based on the fragm entation

2the lim its by a factor ~10, It should be noted th a t a simple rescaling of the flux predictions from top-dow n models, which were m otivated by and based on the energy spectrum observed by AGASA, would reduce the predicted photon flux by only a factor ~ 2 which would still overshoot our experim ental lim it by a factor ~ 5 a t 1019 eV, W hile a m inor contribu tion from top-down models to the observed UHE eosmie-rav flux m ight still be allowed w ithin the lim its derived in th is work, current top-dow n models do not appear to provide an adequate explanation of the origin of the highest-energv cosmic rays (see also Ref. [56] for a com parison of photon flux predictions to the Auger lim its for different top-dow n model param eters).

In acceleration models, photon fluxes are usually expected to be a factor 2 or more below the current bounds (cf. the GZK photon predictions in the Figs. 8 and 9 from Ref. [21]). Such fluxes can be tested w ith fu ture d a ta taken a t the Auger O bservatory (see also Ref. [25]). A fter five years of operation w ith the com plete surface detector, sensitivities a t the level of ~ 4 x 10-4 km -2 sr-1 v r-1 for the in tegrated flux and ~0,7% for the fraction of photons above 20 EeV

2decays may still be compatible with our limits within a factor ^2.

23

Eo [eV]

Fig. 8. The upper limits on the integral flux of photons derived in this work (black arrows) along with predictions from top-down models (SHDM, TD and ZB from Ref. [211, SHDM’ from Ref. [121) and with predictions of the GZK photon flux [211. A flux limit derived indirectly by AG AS A (“A”) is shown for comparison [29].

(95% CL) could be reached.

6 C o n c lu s io n s

Using d a ta from the surface detector we obtained 95% c.l. upper lim its on the photon flux of 3.8 x 10-3 , 2.5 x 10-3 , and 2.2 x 10-3 km -2 sr-1 y r-1 above 1019 eV, 2 x 1019 eV, and 4 x 1019 eV, These are the first direct bounds on the flu x of UHE photons. For the photon fraction, lim its of 2.0%, 5.1%, and 31% were placed.

These lim it improve significantly upon bounds from previous experim ents and p u t strong constraints on certain models of the origin of cosmic rays. C urrent top-dow n models such as the super-heavy dark m a tte r scenario do not appear to provide an adequate explanation of the UHE cosmic rays. In bo ttom -up models of acceleration of nuclear prim aries in astrophysical sources, the ex­pected photon fluxes are typically well below the current bounds. An astro- physical origin of UHE cosmic rays is also suggested by the recent discovery

24

Eo [eV]

Fig. 9. The upper limits on the fraction of photons in the integral cosmic-ray flux de­rived in this work (black arrows) along with previous experimental limits (HP: Hav- erah Park |2K|: A l, A2: AGASA [29,301; AY: AGASA-Yakutsk |31|: Y: Yakutsk |32|: FD: Auger hybrid limit [191). Also shown are predictions from top-down models (SHDM, TD and ZB from Ref. [211, SHDM’ from Ref. [12]) and predictions of the GZK photon fraction [21],

of a correlation of UHE cosmic rays w ith the directions of nearby AGXs |57|, Concerning the m ethod of energy calibration as applied by the Auger Obser­vatory, the photon bounds derived in th is work show th a t there is no strong bias due to a contam ination from UHE photons.

W ith the d a ta accum ulating over the next years, and particu larly when com­plem enting the Auger southern site by an extended northern one, the flux levels expected for GZK photons may be in reach.

Acknowledgements:

The successful insta lla tion and com missioning of the P ierre Auger O bservatory would not have been possible w ithout the strong com m itm ent and effort from the technical and adm inistrative staff in Malargiie,

We are very grateful to the following agencies and organizations for finan­cial support: Comisión Xacional de Energía Atóm ica, Fundación Antorchas, Gobierno De La Provincia de M endoza, M unicipalidad de M alargiie, XDM

25

Holdings and Valle Las Leñas, in g ra titude for the ir eontinuing eooperation over land aeeess, A rgentina; the A ustralian Research Council; Conselho Na­cional de Desenvolvimento Científico e Tecnológico (CN Pq), F inanciadora de Estudos e P ro jetos (F IN E P), Funda§ao de A m paro a Pesquisa do E stado de Rio de Janeiro (FA PE R J), Funda§ao de A m paro a Pesquisa do Estado de Sao Paulo (FA PESP), M inistério de Ciêneia e Tecnología (M CT), Brazil; M in­istry of Education, Y outh and Sports of the Czech Republic; C entre de Calcul IN 2P3/C N R S, C entre N ational de la Recherche Seientifique (CNRS), Con­seil Régional Ile-de-Franee, D épartem ent Physique Nucléaire et Corpusculaire (PN C -IN 2P3/C N R S), D épartem ent Sciences de l ’Univers (SD U -IN SU /CN RS), France; Bundesm inisterium für B ildung und Forschung (BM BF), Deutsche Forschungsgemeinschaft (D FG ), F inanzm inisterium B aden-W ürttem berg, Helm holtz- Gem einschaft Deutscher Forschungszentren (H G F), M inisterium für W issenschaft und Forschung, N ordrhein-W estfalen, M inisterium für W issenschaft, Forschung und K unst, B aden-W ürttem berg, G erm anv; Is titu to Nazionale di F isica Nuele- are (IN FN ), M inistero dell’Istruzione, delPU niversitä e della R icerca (M IIJR),Italy; Consejo Nacional de Ciencia y Tecnología (CO NACY T), Mexico; M in­isterie van Onderwijs, C u ltuu r en W etenschap, N ederlandse O rganisatie voor W etenschappelijk Onderzoek (NW O), Stichting voor Fundam enteel O nder­zoek der M aterie (FOM ), N etherlands; M inistrv of Science and Higher Edu­cation, G ran t Nos. 1 P03 D 014 30, N202 090 31/0623, and PA P/218/2006, Poland; Funda§ao p ara a Ciêneia e a Tecnologia, Portugal; M inistrv for Higher Education, Science, and Technology, Slovenian Research Agencv, Slovenia; Co­m unidad de M adrid, Consejería de Educación de la C om unidad de C astilla La M ancha, FE D E R funds, M inisterio de Educación y Ciencia, X un ta de G ali­cia, Spain; Science and Technology Facilities Council, U nited Kingdom; De­partm en t of Energy, C ontract No, DE-AC02-07CH11359, N ational Science Foundation, G ran t No, 0450696, The G rainger Foundation USA; ALFA-EC / HELEN, European Union 6 th Framework Program , G ran t No, M EIF-C T- 2005-025057, and UNESCO.

References

fll J. Linslev, Phvs. Rev. Lett. 10, 146 (1963).

[21 M.A. Lawrence, R.J.O. Reid, A.A. Watson, J. Phvs. G17, 733 (1991).

[3] D.J. Bird et al, Phvs. Rev. Lett. 71, 3401 (1993).

[4] N. Havashida et al., Phvs. Rev. Lett. 73, 3491 (1994).

[5] R.U. Abbasi et al, Phvs. Lett. B 619, 271 (2005).

[6] Pierre Auger Collaboration, Proc. 29th Intern. Cosmic Rav Conf., Pune, 7, 283(2005).

26

[7] M. Takeda et al., Astropart. Phvs. 19, 447 (2003).

[8] P. Bhattacharjee, G. Sigl, Phvs. Rep. 327, 109 (2000).

[9] S. Sarkar, Acta Phvs. Polon. B35, 351 (2004).

[10] V. Berezinsky, M. Kachelriefi, A. Vilenkin, Phvs. Rev. Lett. 79, 4302 (1997); M. Birkel, S. Sarkar, Astropart. Phvs. 9, 297 (1998); S. Sarkar, R. Toldra, Nucl. Phvs. B 621, 495 (2002); C. Barbot, M. Drees, Astropart. Phvs. 20, 5 (2003); R. Aloisio, V. Berezinsky, M. Kachelriess, Phvs. Rev. D 74, 023516 (2006).

[11] R. Aloisio, V. Berezinsky, M. Kachelriess, Phvs. Rev. D 69, 094023 (2004).

[12] J. Ellis, V. Mayes, D.V. Nanopoulos, Phvs. Rev. D 74, 115003 (2006).

[13] C.T. Hill, Nucl. Phvs. B224, 469 (1983); M.B. Hindmarsh, T.W.B. Kibble, Rep. Prog. Phvs. 58, 477 (1995).

[14] T.J. Weiler, Phvs. Rev. Lett. 49, 234 (1982); T.J. Weiler, Astropart. Phvs. 11, 303 (1999); D. Fargion, B. Mele, A. Salis, Astrophvs. J. 517, 725 (1999)'.

th

[arXiv:astro-ph/0706.2096].

[16] N. Busca, D. Hooper, E.W. Kolb, Phvs. Rev. D 73, 123001 (2006).

[17] V. de Souza, G. Medina-Tanco, J.A. Ortiz, Phvs. Rev. D 72, 103009 (2005).

[18] A.S. Chou, Phvs. Rev. D 74, 103001 (2006).

[19] Pierre Auger Collaboration, Astropart. Phvs. 27, 155 (2007); Pierreth

arXiv:0710.0025 [astro-ph],

[20] K. Greisen, Phvs. Rev. Lett. 16, 748 (1966); G.T. Zatsepin, V.A. Kuzmin, JETP Lett. 4, 78 (1966).

[21] G. Gelmini, O.E. Kalashev, D.V. Semikoz, [arXiv:astro-ph/0506128].

[22] S. Lee, A.V. Olinto, G. Sigl, Astrophvs. J. 455, L21 (1995).

[23] G. Sigl, Phvs. Rev. D 75, 103001 (2007) [arXiv:astro-ph/0703403],

[24] G. Gelmini, O. Kalashev, D.V. Semikoz, [arXiv:astro-ph/0706.2181].

[25] M. Risse, P. Homola, Mod. Phvs. Lett. A 22, 749 (2007).

[26] M. Galaverni, G. Sigl, to appear in Phvs. Rev. Lett., [arXiv:astro-ph/0708.1737]; R. Aloisio, P. Blasi, P. L. Ghia, A. F. Grillo, Phvs. Rev. D 62, 053010 (2000) [arXiv:astro-ph /0001258].

[27] L.D. Landau, I.Ya. Pomeranchuk, Dokl. Akad. Nauk SSSR 92, 535 & 735 (1953);A.B. Migdal, Phvs. Rev. 103, 1811 (1956).

[28] M. Ave et a l, Phvs. Rev. Lett. 85, 2244 (2000); Phvs. Rev. D65, 063007 (2002).

27

[29] K. Shinozaki et al, Astrophvs. J. 571, 1.117 (2002).

[30] M. Risse et al, Phvs. Rev. Lett. 95, 171102 (2005).

[31] G.I. Rubtsov et al., Phvs. Rev. D 73, 063009 (2006).

[32] A.V. Glushkov et a l , JETP Lett. 85, 163 (2007).

[33] Pierre Auger Collaboration, Nucl. Instrum. Meth. A 523, 50 (2004).

th

arXiv:0709.1823 [astro-ph].

[35] X. Bertou, P. Billoir, S. Dagoret-Campagne, Astropart. Phvs. 14, 121 (2000).

[36] X. Bertou et al, P. Auger Collaboration, Nucl. Instrum. Meth. A 568, 839 (2006).

th

(2005).

[38] D. Newton, J. Knapp, A.A. Watson, Astropart. Phvs. 26, 414 (2007).

th

(2005), [arXiv:astro-ph/0507150].

[40] P. Billoir, C. Roucelle, J.C. Hamilton, [arXiv:astro-ph/0701583].

th

arXiv:0706.1105 [astro-ph],th

[43] T. Erber, Rev. Mod. Phvs. 38, 626 (1966); B. McBreen, C.J. Lambert, Phvs. Rev. D 24, 2536 (1981); T. Stanev, H .P Vankov, Phvs. Rev. D 55, 1365(1997); P. Homola et al., Comput. Phvs. Commun. 173, 71 (2005); P. Homola et al, Astropart. Phvs. 27, 174 (2007).

[44] S. Klein, Rev. Mod. Phvs. 71, 1501 (1999); S. Klein, Rad. Phvs. Chem. 75, 696(2006).

[45] S.J. Sciutto, “AIRES: A system for air shower simulations (version 2.2.0),” arXiv:astro-ph/9911331; available at http://www.fisica.unlp.edu.ar/auger/aires

[46] N.N. Kalmykov, S.S. Ostapchenko, A.I. Pavlov, Nucl. Phvs. B (Proc. Suppl.) 52B, 17 (1997).

[47] S. Agostinelli et al, Nucl. Instrum. Meth. A 506, 250 (2003). J. Allison et al, IEEE Transactions on Nuclear Science, 53 270 (2006). See also h ttp ://geant4 .cern .ch/.

th

(2005).

th

Conf., Salt Lake City, 1, 415 (1999).

28

[50] Pierre Auger Collaboration, Proc. 30th Intern. Cosmic Ray Conf., Merida (2007); far Xiv:astro-ph/0706.2096].

[51] E. Oja, International Journal of Neural Systems, 1, 61 (1989).

[52] S. Eidelmann et a l, Particle Data Group, Phvs. Lett. B592, 1 (2004).

[53] M. Risse et al, Czech. J. Phvs. 56, A327 (2006).

[54] T.C. Rogers, M.I. Strikman, J. Phvs. G: Nucl. Part. Phvs. 32, 2041 (2006).

[55] D. Heck et a l, Reports FZK A 6019 & 6097, Forschungszentrum Karlsruhe(1998).

th

arXiv:0706.2960 [astro-ph],

[57] Pierre Auger Collaboration, Science 318, 939 (2007).

29