Search for patterns by combining cosmic-ray energy and arrival directions at the Pierre Auger Observatory

Abstract

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Energy-dependent patterns in the arrival directions of cosmic rays are searched for using data of the Pierre Auger Observatory. We investigate local regions around the highest-energy cosmic rays with ...... eV by analyzing cosmic rays with energies above ...... eV arriving within an angular separation of approximately 15....... We characterize the energy distributions inside these regions by two independent methods, one searching for angular dependence of energy-energy correlations and one searching for collimation of energy along the local system of principal axes of the energy distribution. No significant patterns are found with this analysis. The comparison of these measurements with astrophysical scenarios can therefore be used to obtain constraints on related model parameters such as strength of cosmic-ray deflection and density of point sources.

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Web End = Search for patterns by combining cosmic-ray energy and arrival directions at the Pierre Auger Observatory

The Pierre Auger Collaboration

The Pierre Auger Observatory, Av. San Martn Norte 306, 5613 Malarge, Mendoza, Argentina; http://www.auger.org

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Received: 3 October 2014 / Accepted: 20 May 2015 / Published online: 20 June 2015 The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract Energy-dependent patterns in the arrival directions of cosmic rays are searched for using data of the Pierre Auger Observatory. We investigate local regions around the highest-energy cosmic rays with E 61019 eV by analyz

ing cosmic rays with energies above E 51018 eV arriving

within an angular separation of approximately 15. We characterize the energy distributions inside these regions by two independent methods, one searching for angular dependence of energy-energy correlations and one searching for collimation of energy along the local system of principal axes of the energy distribution. No signicant patterns are found with this analysis. The comparison of these measurements with astrophysical scenarios can therefore be used to obtain constraints on related model parameters such as strength of cosmic-ray deection and density of point sources.

1 Introduction

The long-standing question about the origin and nature of the ultra-high energy cosmic rays (UHECRs) is yet unanswered. Presumably, UHECRs are charged nuclei of extra-galactic origin. They are deected in extragalactic magnetic elds and the magnetic eld of the Milky Way such that their arrival directions may not point back to their sources [1]. The structure, strength, and origin of these cosmic magnetic elds are open questions in astrophysics as well [2,3]. Consequently, UHECRs can also be considered to be probes of the magnetic elds they traverse [4,5] as the deections lead to energy-dependent patterns in their arrival directions, and an analysis of such patterns may allow for conclusions on the strength and structure of the elds.

The Pierre Auger Observatory [6,7] is currently the largest experiment dedicated to observations of UHECRs. In 2007, we reported evidence for a correlation of events with energies above 60 EeV (1 EeV = 1018 eV) with the distribu-

e-mail: mailto:[email protected]

Web End [email protected]

tion of nearby extragalactic matter [8,9]. An update of the analysis yielded a correlation strength which is reduced compared to the initial result [10]. Further searches for anisotropy using variants of autocorrelation functions [11] yielded no statistically-signicant deviation from isotropic scenarios. Following this observation, constraints on the density of point sources and magnetic elds have been reported [12]. Also a direct search for magnetically-induced alignment in the arrival directions of cosmic rays assuming they were protons has been performed without uncovering so-called multiplet structures beyond isotropic expectations [13].

Nevertheless, if the highest-energy cosmic rays with E >60 EeV are tracers of their sources and even if their deection in magnetic elds is dependent on their nuclear charges, some of the lower-energy cosmic rays in a region around them may be of the same origin. From deections both in extragalactic magnetic elds and the magnetic eld of the Milky Way, their distribution of arrival directions may show energy-dependent patterns. In particular a circular blurring of the sources is expected from deection in turbulent magnetic elds, while energy dependent linear structures are expected from deection in coherent magnetic elds.

In this report, we investigate the local regions around cosmic rays with E 60 EeV by analyzing cosmic rays with

energies above E = 5 EeV arriving within an angular sepa

ration of 0.25 rad. The lower energy cut just above the ankle is motivated by the assumption that the selected cosmic rays are predominantly of extragalactic origin. The angular separation cut has been optimized from simulation studies and will be explained below.

We use two methods to characterize the energy distributions inside the local regions. In one method we study energy-energy correlations between pairs of cosmic rays depending on their angular separation from the center of the region. With this measurement we search for signal patterns expected from particle deection in turbulent magnetic elds. In the second method we decompose the directional energy distribution of the cosmic rays along its principal axes. This general decomposition method imposes no requirement on the sign of the

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cosmic-ray charge, or the charge itself. Beyond measuring the strength of collimation along principal axes, the axis directions of the individual regions around the highest-energy cosmic rays potentially reveal local deection patterns due to magnetic elds.

Both methods were originally studied in particle physics, and were referred to as energy-energy correlations and thrust observables, respectively [14,15]. Simulations of their application in cosmic-ray physics have demonstrated the capability to reveal effects from coherent and turbulent magnetic elds [16,17].

This paper is structured as follows. The observables of the energy-energy correlations and the principal-axis analysis are dened in Sect. 2. Their response to structure potentially expected from deection in magnetic elds is illustrated using a simplied model in Sect. 3. The measured distributions of the observables using data of the surface detector of the Pierre Auger Observatory are presented in Sect. 4. In Sect. 5, we rst analyze the directional characteristics of the measured principal axes by studying their reproducibility.We then present a comparison of the measurements with an astrophysical model of UHECR origin and propagation, and determine constraints on the source density, and the strength of cosmic-ray deection as the two dominant model parameters.

2 Denitions

In this section we introduce the main components used for the measurement. We rst dene the local regions in which we analyze the cosmic-ray energies and arrival directions.We then explain the energy-energy correlation observable and its angular dependence. Finally, we present the method of calculating the principal axes of the energy distribution which results in the three values to characterize the strength of collimation along each axis, and the directions of the axes themselves.

2.1 Region of interest

The observables used here are calculated from the events detected in a bounded region in the sky, here denoted as region of interest (ROI). To minimize the statistical penalty from multiple tries, we do not scan the entire sky but investigate a limited number of ROIs located around events with an energy above 60 EeV. This energy cut is motivated by the limitation of the propagation distance by, e.g., the GZK effect [18,19] and corresponds to the energy used in the AGN correlation analysis [8]. The size of the ROIs, i.e. the maximum angular separation of a UHECR belonging to the ROI to the center of the ROI, is set to 0.25 rad. To choose these values we simulated the UHECR propagation in magnetic

elds with the UHECR simulation tool PARSEC [20] for different strengths of the deection and source density. The simulations were analyzed with varying choices of parameters. The chosen values maximize the power of the observables to discriminate between scenarios with strong deections and isotropic scenarios [21,22]. To avoid a possible bias of the characterization of the ROI, we exclude the cosmic ray seeding the ROI from the calculation of the observables.

2.2 Energy-energy correlations

Energy-energy correlations (EECs) are used to obtain information on the turbulent part of galactic and extragalactic magnetic elds [16]. The concept of the EEC was originally developed for tests of quantum chromodynamics (QCD) [14]. The Energy-energy correlation i j is calculated for every pair of UHECRs i, j within a ROI using

i j =

(Ei E(i) ) (E j E(j ) )

Ei E j . (1)

Here Ei is the energy of the UHECR i with the angular separation i to the center of the ROI. Ei(i) is the average

energy of all UHECRs at the angular separation i from the center of the ROI.

The cosmic rays in a ROI can be separated into a signal fraction, whose arrival direction is correlated with the energy, and an isotropic background fraction. The values of i j can be positive or negative depending on the cosmic-ray pair having energies above or below the average energies. An angular ordering is measured in the following sense. A pair of cosmic rays, one being above and the other below the corresponding average energy, results in a negative correlation i j < 0. This is a typical case for a background contribution. A pair with both cosmic rays having energies above or below the average energy at their corresponding angular separation gives a positive correlation i j > 0. Here both signal and background pairs are expected to contribute. As the correlations are determined as a function of the opening angle to the center of the ROI, circular patterns can be found that are expected from turbulent magnetic deections which are sometimes viewed as random-walk propagation.

We present the angular distribution of the EEC as the average distribution of all ROIs. Each value i j is taken into account twice, once at the angular separation i and once at j .

2.3 Principal axes

To further characterize energy-dependent patterns within each individual ROI, we calculate the three principal axes of the energy distribution which we denote as nk=1,2,3. For

this we successively maximize the quantity

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Tk = max

nk

[parenleftBigg][summationtext]

i

|1i pi nk|

i |1i pi| [parenrightBigg]

(2)

with respect to the axes nk starting with k = 1. Here pi is the

cosmic-ray momentum and i the corresponding exposure of the detector [23] in the direction of particle i. The values of Tk=1,2,3 quantify the strength of the collimation of the

particle momenta along each of the three axes nk=1,2,3 of the

principal system. We denote Tk=1,2,3 as thrust observables

following previous studies of perturbative QCD in particle collisions [15,24].

For k = 1 the quantity T1 is called the thrust and con

sequently the rst axis of the principal system n1 is called thrust axis. For the second axis the additional condition n1 n2 is used in Eq. (2). The resulting value T2 is denoted

as thrust major, the axis as thrust-major axis. Finally, the third quantity T3 is called thrust minor with corresponding thrust-minor axis. For the thrust-minor axis n3 it is n1 n2 n3 which renders the maximization in Eq. (2)

trivial. From this denition follows T1 > T2 > T3.

In arbitrarily dened spherical coordinates (r, , ) with orthonormal basis (er, e, e) and the observer at the center, the momenta of the particles at the high energies considered here can be written as pi = |Ei|eri with the energy Ei and

the radial unit vector eri in the arrival direction of particle i. The thrust axis is thus the radial unit vector er pointing to the local barycenter of the energy distribution, and the thrust value is a measure for the energy-weighted strength of clustering of the events. For no dispersion of the particles in the region it takes on the value T1 = 1, whereas for an isotropic

distribution in a circular region the expectation value of T1 depends dominantly on the size of the ROI [22].

The thrust-major and thrust-minor axes can consequently be written as

n2 = cos 2 e + sin 2 e (3)

n3 = cos 3 e + sin 3 e (4) with the angles 2 and 3 = 90 + 2 between the corre

sponding axes and the vector e. Using this together with Eq. (2), the thrust-major T2 becomes maximal if n2 is aligned with a linear distribution of UHECR arrival directions. The thrust-major axis thus points along threadlike structures in the energy distribution of UHECRs. As the thrust minor axis is chosen perpendicular to n1 and n2 it has no physical meaning beyond its connection to the thrust-major axis. However, the thrust-minor T3 gives meaningful information as it denotes the collimation strength perpendicular to the thrust-major axis.

Note that in a perfect isotropic scenario, the energy distribution within the plane dened by n2 and n3 exhibits perfect symmetry. The values of T2 and T3 are approximately equal, and the axis directions are accidental. However, even with

a small signal contribution beyond an isotropic background, the circular symmetry in the (n2, n3) plane is broken giving rise to unequal values of T2 and T3. In addition, the direction of the thrust-major axis then reveals valuable directional information. This directional information can be compared to the direction of deection obtained in a multiplet analysis [13]. However, in contrast to the multiplet analysis the principal axes analysis does not require a uniform charge of the cosmic rays. Its sensitivity is driven by the total deection amount.

3 Benchmark distributions for coherent and turbulent magnetic elds

For obtaining a general understanding of the energy-energy correlations and the thrust observables, we use simple scenarios of cosmic-ray deections in magnetic elds to demonstrate resulting distributions. First we describe the procedure for simulating mock data representing cosmic-ray deection in turbulent and coherent magnetic elds. For different quantitative mixtures of these eld types we then present the distributions of the energy-energy correlations and nally discuss the resulting thrust distributions.

3.1 Simulation procedure

To demonstrate the sensitivity of the observables to deections expected from magnetic elds, we simulate a ROI with UHECRs in a simplied scenario. The deection in cosmic magnetic elds is supposed to result in two different kinds of patterns in the arrival direction of the UHECRs. First, if the UHECRs trajectory resembles a directed random walk, a symmetric blurring of the source is expected. Second, if the particles are deected in large-scale coherent elds, e.g. in the Milky Way, an energy ordering of the UHECRs in threadlike multiplets is expected.

Here we model the distribution of UHECRs in a region around the source as a superposition of both effects. Events in this region of interest are generated in three steps as sketched in Fig. 1. First, the UHECRs are distributed around the center of the ROI following a Fisher distribution [25] with probability density

f (, ) =

4 sinh e( cos) (5)

for angle between cosmic ray and center of the ROI. The Fisher distribution can be considered here as the normal distribution on the sphere. The concentration parameter is chosen with an energy dependence that emulates the deection in turbulent magnetic elds as

= C2TE2. (6)

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(c)

(b)

(a)

Fig. 1 Generation of anisotropically distributed UHECRs in a region of interest. a First, UHECRs are distributed symmetrically around the center of the ROI using a Fisher distribution with energy dependent

concentration parameter according to Eq. (6). b The UHECRs are then deected in one direction using Eq. (8). c UHECRs deected outside of the ROI are moved to a random position inside the region

Fig. 2 Response of the EEC to typical deection patterns from simulations of three different turbulent deection strengths with CT = 0.3 rad EeV (red

squares), CT = 1 rad EeV (blue

upward triangles) andCT = 3 rad EeV (magenta

downward triangles). The dashed line marks the isotropic expectation value according to Eq. (9); black circles denote the result from simulation of isotropically distributed UHECRs

For small deections the distribution resembles a Rayleigh distribution where is related to the root-mean-square RMS of the deection angles by = 2RMS and thus

RMS

CT

E . (7)

A value of CT = 1 rad EeV is equivalent to an RMS of the

deection angle RMS = 5.7 for 10 EeV particles. For exam

ple, using the usual parametrization for deections in turbulent magnetic elds [26,27] this corresponds to the expected deection of 10 EeV protons from a source at a distance D 16 Mpc propagating through a turbulent magnetic eld

with coherence length 1 Mpc and strength B 4nG.

Second, a simple model for the deection in coherent magnetic elds is added on top of the model for turbulent magnetic elds used above. Here the individual cosmic rays are deected in one direction by an angle that depends on the energy of the particles according to

= CC E1 (8)

where the parameter CC is used to model the strength of the coherent deection. The procedure is illustrated in Fig. 1b.

Third, particles deected outside the region of interest are added as a background to keep the number of particles in this setup constant (cf. Fig. 1c). The energies of all events are chosen following a broken power law with spectral index 1 = 2.7 below 40 EeV and 2 = 4.2 above 40 EeV to

be comparable with the observed cosmic-ray energy spectrum [28].

3.2 Response of the energy-energy correlation

The EEC distributions resulting from simulated scenarios using the three values for the turbulent deection strength CT = 0.3, 1.0, 3.0 rad EeV are shown in Fig. 2. As the EEC is

expected to provide only minor sensitivity to coherent deections [16] CC = 0 is used here. For each scenario 50 realiza-

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tions of an ROI with 300 UHECRs have been used, which is approximately the number of UHECRs in a low-coverage region of the measurement presented in Sect. 5. All scenarios are compared with the result for an isotropic distribution of UHECRs. Without structure in the arrival directions of UHECRs, the EEC distribution is at with an expectation value

i j

[angbracketrightbig]

=

(Ei E )

E j E

Ei E j

[angbracketrightBigg] = [parenleftbigg]

1 E

[angbracketleftbigg]

1 E

[angbracketrightbigg][parenrightbigg]2

.

For a source signal the typical signature is an increase towards small angles, as can be seen in Fig. 2. With increasing angular separation the UHECRs average energies decrease, and so do the differences between the UHECR energies and their corresponding average [Eq. (1)]. Consequently, the values

of i j can become small in contrast to a scenario where all UHECR energies contribute at every angular scale. The shape of the EEC distribution in response to a source signal depends on the deection pattern. In general it can be seen that a small deection causes an increase only in the innermost bins, while a larger deection will smear this signature over the whole ROI.

3.3 Response of the principal-axes analysis

(9) In Fig. 3ac the mean and spread of the thrust observables T1,2,3 of 100 realizations of the ROI at each point in the explored parameter space are shown. We used CT = 0.110

rad EeV, without coherent deection, and alternatively with CC = 0.5 rad EeV as well as CC = 1.0 rad EeV.

All three observables are sensitive to a symmetric blurring of the source. For increasing CT the distribution of cos-

(a)

(b)

(c)

(d)

Fig. 3 Response of the thrust observables to typical deection patterns. ac Mean and spread of the observables T1,2,3 as a function of the strength of the deection in turbulent magnetic elds CT. Red circles correspond to no directed deection, green triangles to CC =

0.5 rad EeV and blue squares to CC = 1.0 rad EeV. The shaded area

corresponds to the 1 and 2 expectations of the observables for an isotropic distribution of cosmic rays. d Circular variance of the thrust-major axes calculated in the simulations in 100 ROIs. Gray shading corresponds to the probability density of the expectation value of the circular variance of uniformly-distributed directions

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mic rays in the ROI becomes isotropic, and the observables approach the corresponding expectation value. The value of the thrust major and thrust minor for strong patterns is here below the expectation for no patterns, as the particles are concentrated in the center of the ROI. The thrust minor, Fig. 3c, does not depend on the strength of coherent deection, as the width of the blurring is determined here only by the strength of CT.

When measuring a thrust-major axis of an individual ROI, we also want to determine the stability of the axis direction.As explained in Sect. 2, the thrust major-axis is located in the plane tangential to a sphere around the observer, and provides a directional characteristic on the sky. We quantify the stability of the axis using the circular variance V derived in the specialized statistics for directional data (e.g. [29,30]).The direction of the thrust-major axis n2,i in a region of interest i is dened by the angle i between the axis and the local unit vector e in spherical coordinates with i

[0 . . . ).

To calculate the circular variance V from the n observations i, rst the i are transformed to angles on the full circle by i = i with = 2 owing to the symmetry of

the thrust-major axis. With

C =

n

i=1sin i (10)

the resultant length R is dened as

R = C2 + S2. (11)

Based on the resultant length R in Eq. (11) the circular variance V of a sample of size n is dened as

V = 1

[parenleftbigg]

R n

i=1cos i, S =

n

1/ 2. (12)

In contrast to the variance in linear statistics, V is limited to the interval [0, 1]. The circular variance is a consistent

measure for the concentration of observations on periodic intervals with V = 0 for data from a single direction and

V = 1 for perfectly dispersed data. Even in the limit n

a value V < 1 is also expected for non-directed data as perfect dispersion is unlikely in a random sample.

To demonstrate the strength of correlation of the axes with the direction of deection in the simulation we use the circular variance V among the simulated sample as a measure. The resulting values for the 100 simulated scenarios at every point of the aforementioned parameter space are shown in Fig. 3d. In case of zero coherent deection, and also in case of strong blurring of the sources, no stable axis is found. For small blurring of the sources, the variance between the directions is zero, if there is coherent deection.

4 Measurement

For the measurement of the observables we selected events above 5 EeV recorded with the surface detector of the Pierre Auger Observatory up to March 19, 2013. We require that the zenith angle of the events is smaller than 60 and that the detector stations surrounding the station with the highest signal are active [7]. 30,664 events are included in the analysis; 70 fulll the conditions E 60 EeV and are at least 0.25 rad

inside the eld of view of the Pierre Auger Observatory and therefore seed an ROI.

In order to estimate the uncertainty on the measurement, we repeatedly vary the energy and arrival directions of all events detected with the Pierre Auger Observatory above E = 3 EeV and < 60 within their experimental uncer

tainties and repeat the calculation of the observables with the new values. The mean and spread of the resulting distributions then serve as measured observables and their corresponding uncertainty. The energy resolution of the surface detector is 16 % [31] and the angular resolution of the SD is better than 1 for energies above 5 EeV [32]. The selected

ROIs are kept xed to the original positions in all repetitions. Because of the decreasing spectrum, the number of events in the analysis increases as more events propagate above the lower energy threshold than vice versa. To keep the number of events in the uncertainty analysis xed, the 30,664 events with the highest energy after variation are selected.

In Fig. 4 the distributions of the measured EEC and thrust observables are shown together with the distributions expected from isotropic arrival directions of UHECRs. The goodness-of-t of the measurements compared to expected distributions without structure in the arrival directions of UHECRs, using a 2 test, yields p-values which are all above p = 0.2 except for the thrust minor distribution with

p(T3) = 0.01. Note that the p-value for T3 results from a

lack of signal-like regions in the data which are expected to broaden the distribution. The measured distributions of all four observables reveal thus no local patterns in the arrival directions of UHECRs.

From the principal-axes analysis, a map of the thrust-major axes is derived which is shown in Fig. 5. If not trivial, these axes correspond to the direction of preferred cosmic-ray deections. This question is further studied in the following section.

5 Discussion

In this section we rst continue with analysing the directions of the thrust axes shown as a sky map in Fig. 5. The aim is to search for any individual ROI with signal contributions, e.g. cosmic rays from a point source, by testing the reproducibility of the axis direction. We will then compare

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(a)

(b)

(c)

(d)

Fig. 4 Measurement of the a energy-energy correlation and bd thrust observables T1,2,3 with the Pierre Auger Observatory (red squares and error bars). The measurements are compared to distributions without structure in the arrival directions of UHECRs (gray distributions)

Fig. 5 Hammer projection of the map of principal axes of the directional energy distribution in galactic coordinates. The red shaded areas represent the regions of interest. Black lines denote the second principal

axes (thrust-major axes) n2, black dots mark the positions of the thrust axes n1. The blue shading indicates the exposure of the Pierre Auger Observatory; the dashed line marks the extent of its eld of view

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the measured distributions of the energy-energy correlations and the thrust values in Fig. 4 with astrophysical simulations obtained with the PARSEC Monte Carlo generator. Using these comparisons, limits on the strength of the deection of the UHECRs in extragalactic magnetic elds and the density of point sources of UHECRs are derived.

5.1 Reproducibility of the axes measurement

We further investigate the directional information shown by the thrust-major axes of the individual ROIs in Fig. 5. From the simplied simulations in Sect. 3 we saw that thrust-major directions are reproducible in repeated experiments for scenarios where coherent deections contribute, and turbulent deections are not too large. In additional simulation studies it was shown that evidence for anisotropy could sometimes be found in reproducibility of axis directions even when the thrust scalar values were consistent with isotropy [22].Hence, analysis of the directions of the thrust-major axes could potentially reveal further information.

As we have obtained a single set of measured UHECR data at this point in time, we perform here a stability test on subsets of the data in the following sense. If the measured thrust-major direction obtained in a single ROI is related to a deection pattern reasonably constant in time then the analysis of subsets of the measured data should also reect this pattern. As only a fraction of the ROIs may contain such a deection pattern we perform tests of reproducibility on each ROI individually.

We rst dene the ROIs as before using all available data.

We then split the dataset into n independent subsamples and compare the directions n2,j=1 . . . n2,j=n obtained in each

subsample for every individual region of interest. A low variability of directions in the subsets of the data provides evidence for a non-triviality of the thrust-major axis and consequently for an anisotropic distribution of UHECRs.

The optimal choice for the number of subsamples to split the data into is not known a priori. On the one hand, a large number of n maximizes the number of repeated experiments.On the other hand, as the total number of UHECRs is xed, n = 2 maximizes the number of UHECRs in every sub-

sample. We investigated the choice of n using simulations of the simplied model described in Sect. 3. The test power to distinguish regions of interest containing 600 anisotropically distributed UHECRs from regions with isotropically distributed UHECRs using the circular variance V reaches a plateau for n [greaterorsimilar] 12.

The dependence of the results and their variance with random splits of the data set into 12 parts was investigated. The observed axis directions shown in Fig. 5 were not reproducible in subsets of the data with this analysis. No evidence for a non-triviality of the axes was thus found.

5.2 Limits on propagation parameters

A prime value of the measurements lies in their ability to constrain UHECR propagation scenarios. We outline the procedure to derive limits on scenario parameters using a simple model for extragalactic propagation of protons based on parameterizations as implemented in version 1.2 of the PARSEC software [20]. Although this model is likely too coarse to allow denite conclusions on the sources of UHECRs, it includes at least qualitatively the effects inuencing patterns in the UHECR distributions. Its fast computability allows a scan of a large range of parameter combinations in the source density and the strength of the deection in the extragalactic magnetic eld, thus limiting these important parameters within this model. The procedure to obtain limits from the measurements reported in this paper as outlined here can be applied to any other model.

The PARSEC software simulates ultra-high energy protons by calculating the probability-density function (pdf) to observe a cosmic ray for discrete directions and energies using parameterizations for energy losses and energy-dependent deections. In the calculations, energy losses of the UHECRs from interaction with extragalactic-photon backgrounds, effects from the expansion of the universe and deection in extragalactic magnetic elds are accounted for using parameterizations. To account for deections in the galactic magnetic eld, the calculated pdf is transformed using matrices derived from backtracked UHECRs using the CRT software [33].

As model for the galactic magnetic eld, we use here the model proposed by Jansson and Farrar [34,35]. For the random eld we assume Kolmogorov turbulences with a coherence length Lc = 60 pc and a maximum wavelength

Lmax 260 pc. We use only one realization of the random

component of the model in all simulations. The directions in the simulations are discretized into 49,152 equal-area pixels following the HEALPix layout [36]. The energy is discretized into 100 log-linear spaced bins ranging from 1018.5

to 1020.5 eV. Both choices result in angular and energy bins smaller than the corresponding measurement errors.

We simulated scenarios with unstructured point sources with density and strength of the deection of the cosmic rays

CT = CED (13)

with distance D of the source. We scanned the parameter range CE = 2 200Mpc1/2Eev and source densities up

to = 1 103 Mpc3. We considered contributions from

sources up to a distance Dmax = 2 Gpc. At every point of

the parameter space we simulated sets of 200 pseudo experiments with the same number of events as in the measurement presented in Sect. 4.

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Since the sources of the UHECRs are randomly distributed and have a maximum injection energy Emax = 1000 EeV,

some realizations do not include sources within 43 Mpc, the maximum propagation distance of the most energetic particle in this analysis. Due to the continuous energy loss approximation the maximum distance is here a hard limit and these simulations cannot reproduce the observed energies. To restrict the reported limits to information from the observables such scenarios are not used here. Note that within such a scenario, the necessity of a close source could be used as an additional constraint. The probability of including at least one source in a pdf set can be calculated analytically (e.g. [37]) and is higher than 96 % for source densities greater than = 1 105 Mpc3. Using this argument alone, source

densities with < 1107 Mpc3 may be disfavored. How

ever, the inclusion of this argument only marginally modies the reported limits.

Limits on the strength of the deection and the density of point sources in the simulation are set using the C LS

method [38,39]. Here,

Q = 2 log La

L0 (14)

is the ratio of the likelihood L0 of the data given isotropically

distributed UHECRs, and the likelihood La of the data given

the alternative hypothesis simulated with PARSEC. In the C LS method, not Q directly, but the modied likelihood ratio

C LS =

Pa(Q Qobs)1 P0(Q Qobs)

(15)

is used as test statistic. Here Pa(Q Qobs) is the frequency

with which likelihood ratios Q larger than the observed value are obtained in simulations of the alternative hypothesis and 1 P0(Q Qobs) the corresponding frequency in simula

tions of the null hypothesis. Points in parameter space with C LS < 0.05 are excluded at the 95 % condence level. The resulting limits are shown in Fig. 6 for the individual observables.

(a)

(b)

(c)

(d)

Fig. 6 95 % C LS limits on the strength of the deection of cosmic-ray protons CE [cf. Eqs. (13) and (6) ff.] and density of point sources in simulations using the PARSEC software [20] from the analysis of the a

energy-energy correlations, b thrust, c thrust-major and d thrust-minor distributions. The gray areas are excluded by the measurements

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A combination of the limits is not attempted here as it depends on scenario-specic correlations between the observables. If the cosmic rays are not protons but heavier nuclei the limits are reduced accordingly. For the extreme case that all cosmic rays are iron nuclei with Z = 26 the limits

shift down by more than one order of magnitude. For the proton case shown in Fig. 6 the extragalactic deection of cosmic rays needs to be larger than CE = 10 120Mpc1/2Eev

for source densities smaller than 103 Mpc3 and assuming deections in the galactic magnetic eld as expected from the JanssonFarrar 2012 model with a coherence length set to Lc = 60 pc. The exact value depends on the source density.

Without galactic random eld the limits are only marginally more constraining, choosing a higher coherence length lowers the limits according to the stronger deections.

Previously, we derived from two-point correlations of UHECRs with an energy E > 60 EeV lower bounds on the density of uniformly distributed sources of, e.g., 2

104 Mpc3 if the deection of cosmic rays above 60 EeV is 5 [12]. Only the total deection due to the EGMF and

GMF was taken into account, and no explicit model for the Galactic magnetic eld was used. An approximate comparison with the current analysis can be performed assuming the average deections in the EGMF and GMF add up linearly.The average deection of 60 EeV cosmic rays in the JF2012 eld accounts to 5. The above density therefore gives a lower limit for negligible deections in the EGMF.

With the current analysis we obtain for the lowest EGMF considered a limit of 9104 Mpc3 from an analysis of the

Thrust Minor. We therefore extend the lower bound on the density of uniformly distributed sources by a factor of more than four in the case of small extragalactic deections.

6 Conclusions

In this work, we characterized the distribution of UHECRs with E > 5 EeV in regions of 0.25 rad around events with E > 60 EeV using observables sensitive to patterns characteristic for deections in cosmic magnetic elds. No such patterns have been found within this analysis. We demonstrated the usage of this non-observation to constrain propagation scenarios using a scenario based on parametrizations for the propagation of UHECR protons as an example.

Within the simulated scenario, we estimate that the strength of the deection in the extragalactic magnetic eld has to be larger than CE = 10 120Mpc1/2EeV for

source densities smaller than 103 Mpc3 assuming protons and deections expected from the JanssonFarrar 2012 model for the galactic magnetic eld. For protons with an energy E = 10 EeV from a source at 16 Mpc this trans

lates to a required strength of the deection in extragalactic space of more than 4 if the source density is smaller

than 103 Mpc3 and more than 25 if the source density is smaller than 104 Mpc3.

Acknowledgments The successful installation, commissioning, and operation of the Pierre Auger Observatory would not have been possible without the strong commitment and effort from the technical and administrative staff in Malarge. We are very grateful to the following agencies and organizations for nancial support: Comisin Nacional de Energa Atmica, Fundacin Antorchas, Gobierno De La Provincia de Mendoza, Municipalidad de Malarge, NDM Holdings and Valle Las Leas, in gratitude for their continuing cooperation over land access, Argentina; the Australian Research Council; Conselho Nacional de Desenvolvimento Cientco e Tecnolgico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundao de Amparo Pesquisa do Estado de Rio de Janeiro (FAPERJ), So Paulo Research Foundation (FAPESP) Grants # 2010/07359-6, # 1999/05404-3, Ministrio de Cincia e Tecnologia (MCT), Brazil; MSMT-CR LG13007, 7AMB14AR005, CZ.1.05/2.1.00/03.0058 and the Czech Science Foundation grant 14-17501S, Czech Republic; Centre de Calcul IN2P3/CNRS, Centre National de la Recherche Scientique (CNRS), Conseil Rgional Ile-de-France, Dpartement Physique Nuclaire et Corpusculaire (PNC-IN2P3/CNRS), Dpartement Sciences de lUnivers (SDU-INSU/CNRS), Institut Lagrange de Paris, ILP LABEX ANR-10-LABX-63, within the Investissements dAvenir Programme ANR-11-IDEX-0004-02, France; Bundesministerium fr Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG), Finanzministerium Baden-Wrttemberg, Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ministerium fr Wissenschaft und Forschung, Nordrhein Westfalen, Ministerium fr Wissenschaft, Forschung und Kunst, Baden-Wrttemberg, Germany; Istituto Nazionale di Fisica Nucleare (INFN), Ministero dellIstruzione, dellUniversit e della Ricerca (MIUR), Gran Sasso Center for Astroparticle Physics (CFA), CETEMPS Center of Excellence, Italy; Consejo Nacional de Ciencia y Tecnologa (CONACYT), Mexico; Ministerie van Onderwijs, Cultuur en Wetenschap, Nederlandse Organ-isatie voor Wetenschappelijk Onderzoek (NWO), Stichting voor Fundamenteel Onderzoek der Materie (FOM), Netherlands; National Centre for Research and Development, Grant Nos.ERA-NET-ASPERA/01/11 and ERA-NET-ASPERA/02/11, National Science Centre, Grant Nos. 2013/08/M/ST9/00322, 2013/08/M/ST9/00728 and HARMONIA 5 2013/10/M/ST9/00062, Poland; Portuguese national funds and FEDER funds within COMPETE Programa Operacional Factores de Competitividade through Fundao para a Cincia e a Tecnologia, Portugal; Romanian Authority for Scientic Research ANCS, CNDIUEFISCDI partnership projects nr.20/2012 and nr.194/2012, project nr.1/ASPERA2/2012 ERA-NET, PN-II-RU-PD-2011-3-0145-17, and PN-II-RU-PD-2011-3-0062, the Minister of National Education, Programme for research Space Technology and Advanced Research STAR, project number 83/2013, Romania; Slovenian Research Agency, Slovenia; Comunidad de Madrid, FEDER funds, Ministerio de Educacin y Ciencia, Xunta de Galicia, European Community 7th Framework Program, Grant No. FP7-PEOPLE-2012-IEF-328826, Spain; Science and Technology Facilities Council, United Kingdom; Department of Energy, Contract No. DE-AC02-07CH11359, DE-FR02-04ER41300, DE-FG02-99ER41107 and DE-SC0011689, National Science Foundation, Grant No. 0450696, The Grainger Foundation, USA; NAFOSTED, Vietnam; Marie Curie-IRSES/EPLANET, European Particle Physics Latin American Network, European Union 7th Framework Program, Grant No. PIRSES-2009-GA-246806; and UNESCO.

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References

1. K. Kotera, A.V. Olinto, The astrophysics of ultrahigh energy cosmic rays. Annu. Rev. Astron. Astrophys. 49, 119153 (2011)

2. D. Ryu et al., Magnetic elds in the large-scale structure of the universe. Space Sci. Rev. 166, 135 (2012)

3. L. Widrow et al., The rst magnetic elds. Space Sci. Rev. 166(1), 3770 (2012)

4. S. Lee, A.V. Olinto, G. Sigl, Extragalactic magnetic eld and the highest energy cosmic rays. Astrophys. J. 455, L21L24 (1995)

5. M. Lemoine et al., Ultra-high-energy cosmic-ray sources and large-scale magnetic elds. Astrophys. J. 486.2, L115L118 (1997)6. J. Abraham et al., Properties and performance of the prototype instrument for the Pierre Auger Observatory. Nucl. Instrum. Methods Phys. Res. Sect. A 523, 50 (2004)

7. J. Abraham et al., Trigger and aperture of the surface detector array of the Pierre Auger Observatory. Nucl. Instrum. Methods Phys. Res. Sect. A A613, 2939 (2010)

8. J. Abraham et al., Correlation of the highest energy cosmic rays with nearby extragalactic objects. Science 318, 938943 (2007)

9. J. Abraham et al., Correlation of the highest-energy cosmic rays with the positions of nearby active galactic nuclei. Astropart. Phys. 29, 188204 (2008)

10. P. Abreu et al., Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter. Astropart. Phys. 34, 314326 (2010)

11. P. Abreu et al., A search for anisotropy in the arrival directions of ultra high energy cosmic rays recorded at the Pierre Auger Observatory. J. Cosmol. Astropart. Phys. 4, 040 (2012)

12. P. Abreu et al., Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory. J. Cosmol. Astropart. Phys. 1305, 009 (2013)

13. P. Abreu et al., Search for signatures of magneticallyinduced alignment in the arrival directions measured by the Pierre Auger Observatory. Astropart. Phys. 35, 354361 (2012)

14. C.L. Basham et al., Energy correlations in electronpositron annihilation: testing quantum chromodynamics. Phys. Rev. Lett. 41(23), 15851588 (1978)

15. S. Brandt et al., The principal axis of jetsan attempt to analyse high-energy collisions as two-body processes. Phys. Lett. 12, 57 61 (1964)

16. M. Erdmann, P. Schiffer, A method of measuring cosmic magnetic elds with ultra high energy cosmic ray data. Astropart. Phys. 33, 201205 (2010)

17. M. Erdmann, T. Winchen, Detecting local deection patterns of ultra-high energy cosmic rays using the principal axes of the directional energy distribution. in Proceedings of the 33rd ICRC (Rio de Janeiro, Brasil, 2013)

18. K. Greisen, End to the cosmic-ray spectrum? Phys. Rev. Lett. 16, 748750 (1966)

19. G.T. Zatsepin, V. Kuzmin, Upper limit on the spectrum of cosmic rays. Sov. Phys. JETP Lett. 4, 7880 (1966)

20. H.-P. Bretz et al., PARSEC: a parametrized simulation engine for ultra-high energy cosmic ray protons. Astropart. Phys. 54, 110117 (2014)

21. P. Schiffer, Constraining cosmic magnetic elds by a measurement of energy-energy-correlations with the Pierre Auger Observatory. Ph.D. thesis, RWTH Aachen University (2011)

22. T. Winchen, The principal axes of the directional energy distribution of cosmic rays measured with the Pierre Auger Observatory. Ph.D. thesis, RWTH Aachen University (2013)

23. P. Sommers, Cosmic ray anisotropy analysis with a full-sky observatory. Astropart. Phys. 14, 271286 (2001)

24. E. Farhi, Quantum chromodynamics test for jets. Phys. Rev. Lett.

39(25), 15871588 (1977)

25. R. Fisher, Dispersion on a sphere. Proc. R. Soc. A 217, 295305 (1953)

26. A. Achterberg et al., Intergalactic propagation of UHE cosmic rays. in 19th Texas Symposium on Relativistic Astrophysics and Cosmology, (Paris, France, 1998)

27. D. Harari et al., Lensing of ultra-high energy cosmic rays in turbulent magnetic elds. J. High Energy Phys. 0203, 045 (2002)

28. J. Abraham et al., Measurement of the energy spectrum of cosmic rays above 1018 eV using the Pierre Auger Observatory. Physics Lett. B 685(1018), 239246 (2010)

29. K.V. Mardia, Statistics of Directional Data (Academic Press, London, 1972)

30. S.R. Jammalamadaka, A. SenGupta, Topics in Circular Statistics. Series on multivariate analysis, vol. 5 (World Scientic, Singapore, 2001)

31. C. Di Giulio, Energy calibration of data recorded with the surface detectors of the Pierre Auger Observatory. in Proceedings of the 31st ICRC (d, 2009)

32. C. Bonifazi, A. Letessier-Selvon, E. Santos, A model for the time uncertainty measurements in the Auger surface detector array. Astropart. Phys. 28, 523528 (2008)

33. M.S. Sutherland, B.M. Baughman, J.J. Beatty, CRT: a numerical tool for propagating ultra-high energy cosmic rays through Galactic magnetic eld models. Astropart. Phys. 34, 198204 (2010)

34. R. Jansson, G.R. Farrar, A new model of the Galactic magnetic eld. Astrophys. J. 757, 14 (2012)

35. R. Jansson, G.R. Farrar, The Galactic magnetic eld. Astrophys. J. 761(1), L11 (2012)

36. K.M. Grski et al., HEALPix: a framework for high-resolution discretization and fast analysis of data distributed on the sphere. Astrophys. J. 622, 759771 (2005)

37. S. Chandrasekhar, Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15(1), 189 (1943)

38. A. L. Read, Modied frequentist analysis of search results (the CLs method). in 1st Workshop on Condence Limits (CERN. Geneva, Switzerland, 2000), pp. 81101

39. A.L. Read, Presentation of search results: the CLs technique. J. Phys. G 28(10), 26932704 (2002)

123

269 Page 12 of 15 Eur. Phys. J. C (2015) 75 :269

The Pierre Auger Collaboration

A. Aab42, P. Abreu64, M. Aglietta53, E. J. Ahn81, I. Al Samarai29, I. F. M. Albuquerque17, I. Allekotte1, J. Allen84,P. Allison86, A. Almela8,11, J. Alvarez Castillo57, J. Alvarez-Muiz74, R. Alves Batista41, M. Ambrosio44, A. Aminaei58,L. Anchordoqui80, S. Andringa64, C. Aramo44, V. M. Aranda71, F. Arqueros71, H. Asorey1, P. Assis64, J. Aublin31,M. Ave74, M. Avenier32, G. Avila10, N. Awal84, A. M. Badescu68, K. B. Barber12, J. Buml36, C. Baus36, J. J. Beatty86,K. H. Becker35, J. A. Bellido12, C. Berat32, M. E. Bertaina53, X. Bertou1, P. L. Biermann39, P. Billoir31, S. Blaess12,M. Blanco31, C. Bleve48, H. Blmer36,37, M. Bohov27, D. Boncioli52, C. Bonifazi23, R. Bonino53, N. Borodai62,J. Brack78, I. Brancus65, A. Bridgeman37, P. Brogueira64, W. C. Brown79, P. Buchholz42, A. Bueno73, S. Buitink58,M. Buscemi44, K. S. Caballero-Mora55,e, B. Caccianiga43, L. Caccianiga31, M. Candusso45, L. Caramete39, R. Caruso46,A. Castellina53, G. Cataldi48, L. Cazon64, R. Cester47, A. G. Chavez56, A. Chiavassa53, J. A. Chinellato18, J. Chudoba27,M. Cilmo44, R. W. Clay12, G. Cocciolo48, R. Colalillo44, A. Coleman87, L. Collica43, M. R. Coluccia48, R. Conceio64,F. Contreras9, M. J. Cooper12, A. Cordier30, S. Coutu87, C. E. Covault76, J. Cronin88, A. Curutiu39, R. Dallier34,33,B. Daniel18, S. Dasso3,5, K. Daumiller37, B. R. Dawson12, R. M. de Almeida24, M. De Domenico46, S. J. de Jong58,60,J. R. T. de Mello Neto23, I. De Mitri48, J. de Oliveira24, V. de Souza16, L. del Peral72, O. Deligny29, H. Dembinski37,N. Dhital83, C. Di Giulio45, A. Di Matteo49, J. C. Diaz83, M. L. Daz Castro18, F. Diogo64, C. Dobrigkeit18, W. Docters59,J. C. DOlivo57, A. Dorofeev78, Q. Dorosti Hasankiadeh37, M. T. Dova4, J. Ebr27, R. Engel37, M. Erdmann40,M. Erfani42, C. O. Escobar81,18, J. Espadanal64, A. Etchegoyen8,11, P. Facal San Luis88, H. Falcke58,60,61, K. Fang88,G. Farrar84, A. C. Fauth18, N. Fazzini81, A. P. Ferguson76, M. Fernandes23, B. Fick83, J. M. Figueira8, A. Filevich8,A. Filipi69,70, B. D. Fox89, O. Fratu68, U. Frhlich42, B. Fuchs36, T. Fujii88, R. Gaior31, B. Garca7, S. T. Garcia Roca74,D. Garcia-Gamez30, D. Garcia-Pinto71, G. Garilli46, A. Gascon Bravo73, F. Gate34, H. Gemmeke38, P. L. Ghia31,U. Giaccari23, M. Giammarchi43, M. Giller63, C. Glaser40, H. Glass81, M. Gmez Berisso1, P. F. Gmez Vitale10,P. Gonalves64, J. G. Gonzalez36, N. Gonzlez8, B. Gookin78, J. Gordon86, A. Gorgi53, P. Gorham89, P. Gouffon17,S. Grebe58,60, N. Grifth86, A. F. Grillo52, T. D. Grubb12, F. Guarino44, G. P. Guedes19, M. R. Hampel8, P. Hansen4,D. Harari1, T. A. Harrison12, S. Hartmann40, J. L. Harton78, A. Haungs37, T. Hebbeker40, D. Heck37, P. Heimann42,A. E. Herve37, G. C. Hill12, C. Hojvat81, N. Hollon88, E. Holt37, P. Homola35, J. R. Hrandel58,60, P. Horvath28,M. Hrabovsk27,28, D. Huber36, T. Huege37, A. Insolia46, P. G. Isar66, I. Jandt35, S. Jansen58,60, C. Jarne4, M. Josebachuili8,A. Kp35, O. Kambeitz36, K. H. Kampert35, P. Kasper81, I. Katkov36, B. Kgl30, B. Keilhauer37, A. Keivani87,E. Kemp18, R. M. Kieckhafer83, H. O. Klages37, M. Kleifges38, J. Kleinfeller9, R. Krause40, N. Krohm35, O. Krmer38,D. Kruppke-Hansen35, D. Kuempel40, N. Kunka38, D. LaHurd76, L. Latronico53, R. Lauer91, M. Lauscher40, P. Lautridou34,S. Le Coz32, M. S. A. B. Leo14, D. Lebrun32, P. Lebrun81, M. A. Leigui de Oliveira22, A. Letessier-Selvon31,I. Lhenry-Yvon29, K. Link36, R. Lpez54, A. Lopez Agera74, K. Louedec32, J. Lozano Bahilo73, L. Lu35,75, A. Lucero8,M. Ludwig36, M. Malacari12, S. Maldera53, M. Mallamaci43, J. Maller34, D. Mandat27, P. Mantsch81, A. G. Mariazzi4,V. Marin34, I. C. Maris73, G. Marsella48, D. Martello48, L. Martin33,34, H. Martinez55, O. Martnez Bravo54, D. Martraire29,J. J. Masas Meza3, H. J. Mathes37, S. Mathys35, J. Matthews82, J. A. J. Matthews91, G. Matthiae45, D. Maurel36,D. Maurizio13, E. Mayotte77, P. O. Mazur81, C. Medina77, G. Medina-Tanco57, R. Meissner40, M. Melissas36, D. Melo8,A. Menshikov38, S. Messina59, R. Meyhandan89, S. Mianovi25, M. I. Micheletti6, L. Middendorf40, I. A. Minaya71,L. Miramonti43, B. Mitrica65, L. Molina-Bueno73, S. Mollerach1, M. Monasor88, D. Monnier Ragaigne30, F. Montanet32,C. Morello53, M. Mostaf87, C. A. Moura22, M. A. Muller18,21, G. Mller40, S. Mller37, M. Mnchmeyer31, R. Mussa47,G. Navarra53, S. Navas73, P. Necesal27, L. Nellen57, A. Nelles58,60, J. Neuser35, P. Nguyen12, M. Niechciol42,L. Niemietz35, T. Niggemann40, D. Nitz83, D. Nosek26, V. Novotny26, L. Noka28, L. Ochilo42, A. Olinto88,M. Oliveira64, N. Pacheco72, D. Pakk Selmi-Dei18, M. Palatka27, J. Pallotta2, N. Palmieri36, P. Papenbreer35, G. Parente74,A. Parra74, T. Paul80,85, M. Pech27, J. Pekala62, R. Pelayo54,d, I. M. Pepe20, L. Perrone48, E. Petermann90, C. Peters40,S. Petrera49,50, Y. Petrov78, J. Phuntsok87, R. Piegaia3, T. Pierog37, P. Pieroni3, M. Pimenta64, V. Pirronello46,M. Platino8, M. Plum40, A. Porcelli37, C. Porowski62, R. R. Prado16, P. Privitera88, M. Prouza27, V. Purrello1, E. J. Quel2,S. Querchfeld35, S. Quinn76, J. Rautenberg35, O. Ravel34, D. Ravignani8, B. Revenu34, J. Ridky27, S. Riggi51,74,M. Risse42, P. Ristori2, V. Rizi49, W. Rodrigues de Carvalho74, I. Rodriguez Cabo74, G. Rodriguez Fernandez45,74,J. Rodriguez Rojo9, M. D. Rodrguez-Fras72, D. Rogozin37, G. Ros72, J. Rosado71, T. Rossler28, M. Roth37,E. Roulet1, A. C. Rovero5, S. J. Saf12, A. Saftoiu65, F. Salamida29, H. Salazar54, A. Saleh70, F. Salesa Greus87,G. Salina45, F. Snchez8, P. Sanchez-Lucas73, C. E. Santo64, E. Santos18, E. M. Santos17, F. Sarazin77, B. Sarkar35,R. Sarmento64, R. Sato9, N. Scharf40, V. Scherini48, H. Schieler37, P. Schiffer41, D. Schmidt37, F. G. Schrder37,O. Scholten59, H. Schoorlemmer58,60,89, P. Schovnek27, A. Schulz37, J. Schulz58, J. Schumacher40, S. J. Sciutto4,

123

Eur. Phys. J. C (2015) 75 :269 Page 13 of 15 269

A. Segreto51, M. Settimo31, A. Shadkam82, R. C. Shellard13, I. Sidelnik1, G. Sigl41, O. Sima67, A.mia kowski63,R. mda37, G. R. Snow90, P. Sommers87, J. Sorokin12, R. Squartini9, Y. N. Srivastava85, S. Stani70, J. Stapleton86,J. Stasielak62, M. Stephan40, A. Stutz32, F. Suarez8, T. Suomijrvi29, A. D. Supanitsky5, M. S. Sutherland86, J. Swain85,Z. Szadkowski63, M. Szuba37, O. A. Taborda1, A. Tapia8, M. Tartare32, A. Tepe42, V. M. Theodoro18, C. Timmermans58,60,C. J. Todero Peixoto15, G. Toma65, L. Tomankova37, B. Tom64, A. Tonachini47, G. Torralba Elipe74, D. Torres Machado23,P. Travnicek27, E. Trovato46, M. Tueros74, R. Ulrich37, M. Unger37, M. Urban40, J. F. Valds Galicia57, I. Valio74,L. Valore44, G. van Aar58, P. van Bodegom12, A. M. van den Berg59, S. van Velzen58, A. van Vliet41, E. Varela54,B. Vargas Crdenas57, G. Varner89, J. R. Vzquez71, R. A. Vzquez74, D. Veberi30, V. Verzi45, J. Vicha27, M. Videla8,L. Villaseor56, B. Vlcek72, S. Vorobiov70, H. Wahlberg4, O. Wainberg8,11, D. Walz40, A. A. Watson75, M. Weber38,K. Weidenhaupt40, A. Weindl37, F. Werner36, A. Widom85, L. Wiencke77, B. Wilczyska62, H. Wilczyski62, M. Will37,C. Williams88, T. Winchen35, D. Wittkowski35, B. Wundheiler8, S. Wykes58, T. Yamamoto88,a, T. Yapici83, G. Yuan82,A. Yushkov42, B. Zamorano73, E. Zas74, D. Zavrtanik69,70, M. Zavrtanik69,70, I. Zaw84,c, A. Zepeda55,b, J. Zhou88,Y. Zhu38, M. Zimbres Silva18, M. Ziolkowski42, F. Zuccarello46

1 Centro Atmico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina

2 Centro de Investigaciones en Lseres y Aplicaciones, CITEDEF and CONICET, Villa Martelli, Buenos Aires, Argentina

3 Departamento de Fsica, FCEyN Universidad de Buenos Aires y CONICET, Buenos Aires, Argentina

4 IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina

5 Instituto de Astronoma y Fsica del Espacio (CONICET-UBA), Buenos Aires, Argentina

6 Instituto de Fsica de Rosario (IFIR) - CONICET/U.N.R. and Facultad de Ciencias Bioqumicas y Farmacuticas U.N.R., Rosario, Argentina

7 Instituto de Tecnologas en Deteccin y Astropartculas (CNEA, CONICET, UNSAM) and National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentina

8 Instituto de Tecnologas en Deteccin y Astropartculas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina

9 Observatorio Pierre Auger, Malarge, Argentina

10 Observatorio Pierre Auger and Comisin Nacional de Energa Atmica, Malarge, Argentina

11 Universidad Tecnolgica Nacional - Facultad Regional Buenos Aires, Buenos Aires, Argentina

12 University of Adelaide, Adelaide, SA, Australia

13 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil

14 Faculdade Independente do Nordeste, Vitria da Conquista, Brazil

15 Universidade de So Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil

16 Instituto de Fsica de So Carlos, Universidade de So Paulo, So Carlos, SP, Brazil

17 Instituto de Fsica, Universidade de So Paulo, So Paulo, SP, Brazil

18 Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil

19 Universidade Estadual de Feira de Santana, Feira de Santana, Brazil

20 Universidade Federal da Bahia, Salvador, BA, Brazil

21 Universidade Federal de Pelotas, Pelotas, RS, Brazil

22 Universidade Federal do ABC, Santo Andr, SP, Brazil

23 Instituto de Fsica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

24 Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil

25 Rudjer Bokovi Institute, 10000 Zagreb, Croatia

26 Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Republic

27 Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic

28 Palacky University, RCPTM, Olomouc, Czech Republic

29 Institut de Physique Nuclaire dOrsay (IPNO), Universit Paris 11, CNRS-IN2P3, Orsay, France

30 Laboratoire de lAcclrateur Linaire (LAL), Universit Paris 11, CNRS-IN2P3, Orsay, France

31 Laboratoire de Physique Nuclaire et de Hautes Energies (LPNHE), Universits Paris 6 et Paris 7, CNRS-IN2P3, Paris, France

32 Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit Grenoble-Alpes, CNRS/IN2P3, Grenoble, France

33 Station de Radioastronomie de Nanay, Observatoire de Paris, CNRS/INSU, Nanay, France

34 SUBATECH, cole des Mines de Nantes, CNRS-IN2P3, Universit de Nantes, Nantes, France

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35 Bergische Universitt Wuppertal, Wuppertal, Germany

36 Karlsruhe Institute of Technology - Campus South - Institut fr Experimentelle Kernphysik (IEKP), Karlsruhe, Germany

37 Karlsruhe Institute of Technology - Campus North - Institut fr Kernphysik, Karlsruhe, Germany

38 Karlsruhe Institute of Technology - Campus North - Institut fr Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany

39 Max-Planck-Institut fr Radioastronomie, Bonn, Germany

40 RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany

41 Universitt Hamburg, Hamburg, Germany

42 Universitt Siegen, Siegen, Germany

43 Universit di Milano and Sezione INFN, Milan, Italy

44 Universit di Napoli Federico II and Sezione INFN, Napoli, Italy

45 Universit di Roma II Tor Vergata and Sezione INFN, Roma, Italy

46 Universit di Catania and Sezione INFN, Catania, Italy

47 Universit di Torino and Sezione INFN, Torino, Italy

48 Dipartimento di Matematica e Fisica E. De Giorgi dellUniversit del Salento and Sezione INFN, Lecce, Italy

49 Dipartimento di Scienze Fisiche e Chimiche dellUniversit dellAquila and INFN, LAquila, Italy

50 Gran Sasso Science Institute (INFN), LAquila, Italy

51 Istituto di Astrosica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy

52 INFN, Laboratori Nazionali del Gran Sasso, Assergi, LAquila, Italy

53 Osservatorio Astrosico di Torino (INAF), Universit di Torino and Sezione INFN, Torino, Italy

54 Benemrita Universidad Autnoma de Puebla, Puebla, Mexico

55 Centro de Investigacin y de Estudios Avanzados del IPN (CINVESTAV), Mexico, Mexico

56 Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexico

57 Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexico

58 IMAPP, Radboud University Nijmegen, Nijmegen, Netherlands

59 KVI - Center for Advanced Radiation Technology, University of Groningen, Groningen, Netherlands

60 Nikhef, Science Park, Amsterdam, Netherlands

61 ASTRON, Dwingeloo, Netherlands

62 Institute of Nuclear Physics PAN, Krakow, Poland

63 University of d, d, Poland

64 Laboratrio de Instrumentao e Fsica Experimental de Partculas - LIP and Instituto Superior Tcnico - IST, Universidade de Lisboa - UL, Lisbon, Portugal

65 Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania

66 Institute of Space Sciences, Bucharest-Magurele, Romania

67 Physics Department, University of Bucharest, Bucharest, Romania

68 University Politehnica of Bucharest, Bucharest, Romania

69 Experimental Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia

70 Laboratory for Astroparticle Physics, University of Nova Gorica, Nova Gorica, Slovenia

71 Universidad Complutense de Madrid, Madrid, Spain

72 Universidad de Alcal, Alcal de Henares, Madrid, Spain

73 Universidad de Granada and C.A.F.P.E., Granada, Spain

74 Universidad de Santiago de Compostela, Santiago de Compostela, Spain

75 School of Physics and Astronomy, University of Leeds, Leeds, UK

76 Case Western Reserve University, Cleveland, OH, USA

77 Colorado School of Mines, Golden, CO, USA

78 Colorado State University, Fort Collins, CO, USA

79 Colorado State University, Pueblo, CO, USA

80 Department of Physics and Astronomy, , City University of New York, New York, USA

81 Fermilab, Batavia, IL, USA

82 Louisiana State University, Baton Rouge, LA, USA

83 Michigan Technological University, Houghton, MI, USA

84 New York University, New York, NY, USA

85 Northeastern University, Boston, MA, USA

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86 Ohio State University, Columbus, OH, USA

87 Pennsylvania State University, University Park, PA, USA

88 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA

89 University of Hawaii, Honolulu, HI, USA

90 University of Nebraska, Lincoln, NE, USA

91 University of New Mexico, Albuquerque, NM, USA

a Now at Konan University

b Also at the Universidad Autonoma de Chiapas on leave of absence from Cinvestav

c Now at NYU Abu Dhabi

d Now at Unidad Profesional Interdisciplinaria de Ingeniera y Tecnologas Avanzadas del IPN, Mxico, D.F., Mxico

e Now at Universidad Autnoma de Chiapas, Tuxtla Gutirrez, Chiapas, Mxico

Deceased

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