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Correlations with nearby AGN measured by the Pierre Auger Observatory
Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173 www.elsevierphysics.com
Correlations with nearby AGN measured by the Pierre Auger Observatory Esteban Roulet, for the Pierre Auger Collaborationa a
CONICET, Centro At´omico Bariloche, Av. Bustillo 9500, Bariloche, 8400, Argentina
We discuss the recent results of the Pierre Auger Observatory showing a correlation between the highest energy cosmic rays and the nearby extragalactic matter distribution. This was established from a comparison of the arrival directions detected and the positions of the known AGNs. By performing a scan over the maximum angular separation, the maximum AGN redshift and the threshold energy considered, the largest significance was obtained for angles of 3.2◦ , distances of 71 Mpc and energies above 57 EeV, for which 20 events out of 27 are found to be in correlation, while on average only 5.6 were expected to be correlated by chance if the distribution was isotropic. In general the correlation is significant for angles smaller than 6◦ and distances up to 100 Mpc. This indicates that the highest energy cosmic rays are extragalactic and supports the conclusion that the observed suppression in the cosmic ray spectrum at the highest energies is indeed due to the GZK effect rather than to the exhaustion of the acceleration power of the sources.
The Pierre Auger Observatory was built with the purpose of clarifying what is the nature and which are the sources of the ultra-high energy cosmic rays (UHECRs). It has already obtained interesting constraints on the photon and neutrino fluxes [1,2], excluding to a large extent the so-called top down models, and hence providing additional support to the scenarios in which the CRs are hadronic (protons or heavier nuclei) that get accelerated in a bottom up way in some astrophysical sources. Moreover, the observation [3,4] of a suppression in the CR spectrum above 40 EeV (where 1 EeV ≡ 1018 eV) is consistent with the expected attenuation associated to the energy losses of the CRs when they interact with the CMB photons during their propagation, the GZK effect [5]. The dream of directly identifying the cosmic ray sources may become a reality at the highest energies due to the fact that in this energy regime the deflections of charged particles in the astrophysical magnetic fields could become small, and also because due to the GZK effect only relatively nearby sources contribute to the CR fluxes. Indeed, the deflection of a particle with charge Z
0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.084
traversing a distance L in a magnetic field B is L dx × B ◦ 60 EeV (1) δ 2.7 Z . 0 kpc 3μG E Hence, for the characteristic values of the galactic magnetic field of a few μG being coherent over scales of ∼ 1 kpc the deflections should be of just a few degrees for protons with E > 60 EeV. For heavier nuclei, since the deflections increase proportionally to their charges the CR astronomy will be quite difficult in this case unless the extent of the regular magnetic fields above the galactic plane is well below 1 kpc. Extragalactic magnetic fields are much more uncertain, but it is quite likely that the deflections they induce are smaller than those produced by the galactic fields. Regarding the source distances, due to the GZK attenuation the protons with E > 60 EeV can only arrive from sources within ∼ 200 Mpc (this is the so-called GZK horizon, defined as the distance within which 90% of the CRs arriving with energies above a given threshold Eth are expected to be produced [6]). For Eth = 80 EeV, the corresponding GZK horizon is about 90 Mpc. In the case of Fe nuclei, for which the main process responsible for their attenuation is photodisintegration (rather than the photopion produc-
170
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
tion which attenuates the protons), the horizons turn out to be comparable to the proton ones, but for intermediate mass nuclei the horizons are actually smaller. In view of all this and of the fact that the nearby distribution of matter is quite inhomogeneous, with galaxies being clustered in structures like the super-galactic plane, it is to be expected that the distribution of UHECR arrival directions will inherit the anisotropies of the distribution of their sources. Confronting the CR arrival direction distribution with the location of their potential sources, for which the active galactic nuclei (AGN) and the gamma ray bursts (GRBs) are two of the favorite candidates, can also be a very efficient way to establish an anisotropy signal. With this in mind, the Auger Collaboration performed a search for correlations between the arrival directions of the highest energy events and the location of the known nearby AGN (as compiled in the latest edition of the V´eron Cetty and V´eron catalog (VC catalog)). The results of this search for correlations were published in [7,8], based on the events measured by the Auger surface detector during its construction phase since January 2004 until August 2007. Events with zenith angles smaller than 60◦ are considered, requiring as quality criterium that five out of the six detector units surrounding the detector with the largest signal are active, and that the reconstructed shower core lies within an active triangle of stations. This amounts to a total exposure of about 9000 km2 sr yr, which is approximately 1.3 years of the exposure for the complete array with 3000 km2 . The angular resolution at the highest energies considered here is better than 1◦ . Since the exact energy threshold Eth above which a strong correlation could be expected is not known a priori due to the poorly known CR composition and also due to the systematic uncertainties affecting the CR energy determination, a scan over Eth above 40 EeV was performed. Also since the CR deflections are a priori unknown due to the uncertain size and extent of the intervening magnetic fields as well as of the CR charges, a scan over the angular separation Ψ between events and AGN directions was per-
formed in the range from 1◦ , which is approximately the angular resolution at these energies, up to 8◦ , since for larger angles the probability of having correlations by chance becomes quite large. Finally, given the uncertain GZK horizon a scan over the maximum AGN redshift zmax up to a value of 0.024, corresponding to a distance of about 100 Mpc, was performed. Larger values of zmax were not considered because the VC catalog becomes quite incomplete and inhomogeneous beyond those distances. For any specified combination of these three parameters, Eth , Ψ and zmax , we obtain the probability P that an isotropic distribution of N events (the number of events present in the data above Eth ) gives rise to a number of correlations (i.e. of events separated by an angle smaller than Ψ from an AGN at redshift smaller than zmax ) larger or equal than the number of correlations, k, found in the data. This is just P =
N N j=k
j
pj (1 − p)N −j ,
(2)
where p is the probability that an individual isotropic event correlates. The quantity p is just the fraction of the sky visible to the Auger Observatory, weighted by the experimental exposure, which is covered by circles of radius Ψ around each AGN closer than zmax . Performing the above mentioned scan, the minimum value of P , Pmin , is obtained for Eth = 57 EeV (i.e. for the 27 highest energy events), for Ψ = 3.2◦ and for zmax = 0.017, which corresponds to a maximum AGN distance of ∼ 71 Mpc. Note that for these values the individual isotropic probability is p 0.21. The fraction of isotropic simulations which under a similar scan give rise to values of P smaller than Pmin is ∼ 10−5 . This shows that there is indeed a sizeable correlation between the highest energy events observed and the directions towards nearby AGN. We note that the values of P remain small actually for a range of separations Ψ between 2◦ and 6◦ , and for zmax from 0.013 up to 0.024, as is illustrated in fig. 1, which shows the values of P in slices of the parameter space containing the absolute minimum (i.e. scanning in just one pa-
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
171
Figure 1. Probability for the null hypothesis (isotropy) vs. Ψ, zmax and Eth . In each case the other two parameters are kept fixed at the values leading to the minimum probability (Ψ = 3.2◦ , zmax = 0.017 and Eth = 57 EeV). rameter in each case, leaving the other two at the values leading to Pmin ). It is also seen that for Eth < 57 EeV there is a steep rise in the probabilities, what may be associated to the abrupt increase in the horizon size below the GZK threshold energy, what leads to a sudden isotropisation of the arrival directions distribution. It is worth noting that this threshold energy coincides with the value at which the measured spectrum falls to half the value obtained from a power law extrapolation of the spectrum observed below 40 EeV [4], and is also the energy at which a maximal anisotropy signature is observed looking at the autocorrelation function of the events [9]. The angular scale of 3.2◦ obtained also suggests that the CR deflections are not large, although it is important to keep in mind that the closest AGN to an event need not be its source. Actually, it could well be that the AGN considered are just acting as tracers of the nearby large scale structure and the real sources are not AGN but some other astrophysical objects having a similar spatial distribution, such as GRBs, or it could also be that the actual sources are a particular subset of the AGN compiled in the VC catalog, or even some obscured AGN could be contributing too.
The map of the arrival directions of the 27 highest energy events together with the location of the 442 AGN (292 within the field of view of Auger) closer than 71 Mpc is displayed in fig. 2. Each event is indicated with a circle of 3.2◦ radius and it is found that 20 out of the 27 events with E > 57 EeV have an AGN within its associated circle. It is interesting to note that 5 out of the 7 events which do not correlate within these parameters are close to the galactic plane, at galactic latitudes |b| < 12◦ , a region in which the VC catalog is known to be largely incomplete due to obscuration effects. It is also interesting to note that two events fall within 3.2◦ of Centaurus A, the closest powerful active galaxy, lying at less than 4 Mpc from us in the direction (, b) = (−51.5◦ , 19.4◦ ). The clustering of events around this region and near the super-galactic plane (dashed line) is also apparent. The history of the finding just described actually proceeded in two steps: using initially data until the end of May 2006 the first indications of correlations were obtained with a set of parameters corresponding to E > 56 EeV, Ψ = 3.1◦ and zmax = 0.018 (which are quite similar to those just discussed). In the second stage, a prescrip-
172
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
Figure 2. Map in galactic coordinates with the positions of the AGN within 71 Mpc (stars) and the 27 events with E > 57 EeV (circles of 3.2◦ radius). Shading indicates regions of equal exposure. tion was defined to establish with further confidence this hint of correlation and to assign an unambiguous a priori significance to the anisotropy observed using an independent data set. This procedure consisted in fixing the values of the parameters to those giving the minimum probability Pmin in the initial search and then studying the resulting correlation signal with those fixed parameters (i.e. without rescanning). Once the isotropic null hypothesis got rejected with more than 99% CL (taking into account the running nature of the prescription, i.e. the fact that after each new event the correlation probability was evaluated) the test was considered successful. In this way isotropy was rejected with the new data set alone at more than 99% CL since in the data collected after the initial search, and up to end of August 2007, 8 out of 13 events were in correlation, while only 2.7 were expected on average from an isotropic distribution. It may be noted that the fact that the VC catalog is not complete nor uniform has absolutely
no relevance for the significance of this test. On the other hand, it is also important that the binomial probability scan performed does not test for an overall global proportionality across the sky between the events and a particular source model based on the AGN distribution, and hence the incompleteness of this catalog is not an obstacle to establish the presence of a correlation (eventually one could expect to just miss some correlations due to the catalog incompleteness, but not to enhance them). Another feature that has been pointed out in [8] is the apparent paucity of events from the region of the Virgo cluster (no events with E > 57 EeV fall within 20◦ of the location of M87 at (, b) = (−76.2◦ , 74.5◦ )). It has to be taken into account that Virgo is however in a comparatively low exposure region (with about 3 times smaller exposure than the Cen A region) and that being the Virgo cluster quite nearby, at less than 20 Mpc, a large fraction of the AGN cataloged in this region are quite faint, and are hence probably
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
not particularly good candidate sites for UHECR acceleration. There are also many comparably faint AGN farther away which are below the sensitivity of the surveys and are hence not included in the VC catalog. It will be anyhow interesting to keep looking into the possible absence of events from Virgo with enlarged future data sets. In conclusion, the Auger Observatory has found a significant correlation between the arrival directions of the highest energy events, with E > 57 EeV, and the distribution of the nearby structures within ∼ 100 Mpc. This was established by correlating the events with the distribution of known AGN. This gives a strong support to the idea that above the ankle the CRs are of extragalactic origin. Moreover, it suggests that the observed attenuation in the CR spectrum above 40 EeV is indeed due to the GZK effect, and not just to the exhaustion of the acceleration power of the sources. This also suggests that we may be at the beginning of the era of charged particle astronomy. REFERENCES 1. The Pierre Auger Collaboration, Astropart. Phys. 29 (2008) 243-256 2. The Pierre Auger Collaboration, Phys. Rev. Lett. 100 (2008) 211101 3. R. U. Abbasi et al. (HiRes Collaboration), Phys. Rev. Lett. 100 (2008) 101101 4. The Pierre Auger Collaboration, Phys. Rev. Lett. 101 (2008) 061101 5. K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G. T. Zatsepin and V. A. Kuzmin, JETP Lett. 4 (1966) 78. 6. D. Harari, S. Mollerach, E. Roulet, JCAP 0611:012 (2006) 7. The Pierre Auger Collaboration, Science 318 (2007) 939-943 8. The Pierre Auger Collaboration, Astropart. Phys. 29 (2008) 188-204 9. S. Mollerach, for the Pierre Auger Collaboration, (2007) arxiv:0706.1749 [astro-ph]
173
Correlations with nearby AGN measured by the Pierre Auger Observatory Esteban Roulet, for the Pierre Auger Collaborationa a
CONICET, Centro At´omico Bariloche, Av. Bustillo 9500, Bariloche, 8400, Argentina
We discuss the recent results of the Pierre Auger Observatory showing a correlation between the highest energy cosmic rays and the nearby extragalactic matter distribution. This was established from a comparison of the arrival directions detected and the positions of the known AGNs. By performing a scan over the maximum angular separation, the maximum AGN redshift and the threshold energy considered, the largest significance was obtained for angles of 3.2◦ , distances of 71 Mpc and energies above 57 EeV, for which 20 events out of 27 are found to be in correlation, while on average only 5.6 were expected to be correlated by chance if the distribution was isotropic. In general the correlation is significant for angles smaller than 6◦ and distances up to 100 Mpc. This indicates that the highest energy cosmic rays are extragalactic and supports the conclusion that the observed suppression in the cosmic ray spectrum at the highest energies is indeed due to the GZK effect rather than to the exhaustion of the acceleration power of the sources.
The Pierre Auger Observatory was built with the purpose of clarifying what is the nature and which are the sources of the ultra-high energy cosmic rays (UHECRs). It has already obtained interesting constraints on the photon and neutrino fluxes [1,2], excluding to a large extent the so-called top down models, and hence providing additional support to the scenarios in which the CRs are hadronic (protons or heavier nuclei) that get accelerated in a bottom up way in some astrophysical sources. Moreover, the observation [3,4] of a suppression in the CR spectrum above 40 EeV (where 1 EeV ≡ 1018 eV) is consistent with the expected attenuation associated to the energy losses of the CRs when they interact with the CMB photons during their propagation, the GZK effect [5]. The dream of directly identifying the cosmic ray sources may become a reality at the highest energies due to the fact that in this energy regime the deflections of charged particles in the astrophysical magnetic fields could become small, and also because due to the GZK effect only relatively nearby sources contribute to the CR fluxes. Indeed, the deflection of a particle with charge Z
0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.084
traversing a distance L in a magnetic field B is L dx × B ◦ 60 EeV (1) δ 2.7 Z . 0 kpc 3μG E Hence, for the characteristic values of the galactic magnetic field of a few μG being coherent over scales of ∼ 1 kpc the deflections should be of just a few degrees for protons with E > 60 EeV. For heavier nuclei, since the deflections increase proportionally to their charges the CR astronomy will be quite difficult in this case unless the extent of the regular magnetic fields above the galactic plane is well below 1 kpc. Extragalactic magnetic fields are much more uncertain, but it is quite likely that the deflections they induce are smaller than those produced by the galactic fields. Regarding the source distances, due to the GZK attenuation the protons with E > 60 EeV can only arrive from sources within ∼ 200 Mpc (this is the so-called GZK horizon, defined as the distance within which 90% of the CRs arriving with energies above a given threshold Eth are expected to be produced [6]). For Eth = 80 EeV, the corresponding GZK horizon is about 90 Mpc. In the case of Fe nuclei, for which the main process responsible for their attenuation is photodisintegration (rather than the photopion produc-
170
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
tion which attenuates the protons), the horizons turn out to be comparable to the proton ones, but for intermediate mass nuclei the horizons are actually smaller. In view of all this and of the fact that the nearby distribution of matter is quite inhomogeneous, with galaxies being clustered in structures like the super-galactic plane, it is to be expected that the distribution of UHECR arrival directions will inherit the anisotropies of the distribution of their sources. Confronting the CR arrival direction distribution with the location of their potential sources, for which the active galactic nuclei (AGN) and the gamma ray bursts (GRBs) are two of the favorite candidates, can also be a very efficient way to establish an anisotropy signal. With this in mind, the Auger Collaboration performed a search for correlations between the arrival directions of the highest energy events and the location of the known nearby AGN (as compiled in the latest edition of the V´eron Cetty and V´eron catalog (VC catalog)). The results of this search for correlations were published in [7,8], based on the events measured by the Auger surface detector during its construction phase since January 2004 until August 2007. Events with zenith angles smaller than 60◦ are considered, requiring as quality criterium that five out of the six detector units surrounding the detector with the largest signal are active, and that the reconstructed shower core lies within an active triangle of stations. This amounts to a total exposure of about 9000 km2 sr yr, which is approximately 1.3 years of the exposure for the complete array with 3000 km2 . The angular resolution at the highest energies considered here is better than 1◦ . Since the exact energy threshold Eth above which a strong correlation could be expected is not known a priori due to the poorly known CR composition and also due to the systematic uncertainties affecting the CR energy determination, a scan over Eth above 40 EeV was performed. Also since the CR deflections are a priori unknown due to the uncertain size and extent of the intervening magnetic fields as well as of the CR charges, a scan over the angular separation Ψ between events and AGN directions was per-
formed in the range from 1◦ , which is approximately the angular resolution at these energies, up to 8◦ , since for larger angles the probability of having correlations by chance becomes quite large. Finally, given the uncertain GZK horizon a scan over the maximum AGN redshift zmax up to a value of 0.024, corresponding to a distance of about 100 Mpc, was performed. Larger values of zmax were not considered because the VC catalog becomes quite incomplete and inhomogeneous beyond those distances. For any specified combination of these three parameters, Eth , Ψ and zmax , we obtain the probability P that an isotropic distribution of N events (the number of events present in the data above Eth ) gives rise to a number of correlations (i.e. of events separated by an angle smaller than Ψ from an AGN at redshift smaller than zmax ) larger or equal than the number of correlations, k, found in the data. This is just P =
N N j=k
j
pj (1 − p)N −j ,
(2)
where p is the probability that an individual isotropic event correlates. The quantity p is just the fraction of the sky visible to the Auger Observatory, weighted by the experimental exposure, which is covered by circles of radius Ψ around each AGN closer than zmax . Performing the above mentioned scan, the minimum value of P , Pmin , is obtained for Eth = 57 EeV (i.e. for the 27 highest energy events), for Ψ = 3.2◦ and for zmax = 0.017, which corresponds to a maximum AGN distance of ∼ 71 Mpc. Note that for these values the individual isotropic probability is p 0.21. The fraction of isotropic simulations which under a similar scan give rise to values of P smaller than Pmin is ∼ 10−5 . This shows that there is indeed a sizeable correlation between the highest energy events observed and the directions towards nearby AGN. We note that the values of P remain small actually for a range of separations Ψ between 2◦ and 6◦ , and for zmax from 0.013 up to 0.024, as is illustrated in fig. 1, which shows the values of P in slices of the parameter space containing the absolute minimum (i.e. scanning in just one pa-
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
171
Figure 1. Probability for the null hypothesis (isotropy) vs. Ψ, zmax and Eth . In each case the other two parameters are kept fixed at the values leading to the minimum probability (Ψ = 3.2◦ , zmax = 0.017 and Eth = 57 EeV). rameter in each case, leaving the other two at the values leading to Pmin ). It is also seen that for Eth < 57 EeV there is a steep rise in the probabilities, what may be associated to the abrupt increase in the horizon size below the GZK threshold energy, what leads to a sudden isotropisation of the arrival directions distribution. It is worth noting that this threshold energy coincides with the value at which the measured spectrum falls to half the value obtained from a power law extrapolation of the spectrum observed below 40 EeV [4], and is also the energy at which a maximal anisotropy signature is observed looking at the autocorrelation function of the events [9]. The angular scale of 3.2◦ obtained also suggests that the CR deflections are not large, although it is important to keep in mind that the closest AGN to an event need not be its source. Actually, it could well be that the AGN considered are just acting as tracers of the nearby large scale structure and the real sources are not AGN but some other astrophysical objects having a similar spatial distribution, such as GRBs, or it could also be that the actual sources are a particular subset of the AGN compiled in the VC catalog, or even some obscured AGN could be contributing too.
The map of the arrival directions of the 27 highest energy events together with the location of the 442 AGN (292 within the field of view of Auger) closer than 71 Mpc is displayed in fig. 2. Each event is indicated with a circle of 3.2◦ radius and it is found that 20 out of the 27 events with E > 57 EeV have an AGN within its associated circle. It is interesting to note that 5 out of the 7 events which do not correlate within these parameters are close to the galactic plane, at galactic latitudes |b| < 12◦ , a region in which the VC catalog is known to be largely incomplete due to obscuration effects. It is also interesting to note that two events fall within 3.2◦ of Centaurus A, the closest powerful active galaxy, lying at less than 4 Mpc from us in the direction (, b) = (−51.5◦ , 19.4◦ ). The clustering of events around this region and near the super-galactic plane (dashed line) is also apparent. The history of the finding just described actually proceeded in two steps: using initially data until the end of May 2006 the first indications of correlations were obtained with a set of parameters corresponding to E > 56 EeV, Ψ = 3.1◦ and zmax = 0.018 (which are quite similar to those just discussed). In the second stage, a prescrip-
172
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
Figure 2. Map in galactic coordinates with the positions of the AGN within 71 Mpc (stars) and the 27 events with E > 57 EeV (circles of 3.2◦ radius). Shading indicates regions of equal exposure. tion was defined to establish with further confidence this hint of correlation and to assign an unambiguous a priori significance to the anisotropy observed using an independent data set. This procedure consisted in fixing the values of the parameters to those giving the minimum probability Pmin in the initial search and then studying the resulting correlation signal with those fixed parameters (i.e. without rescanning). Once the isotropic null hypothesis got rejected with more than 99% CL (taking into account the running nature of the prescription, i.e. the fact that after each new event the correlation probability was evaluated) the test was considered successful. In this way isotropy was rejected with the new data set alone at more than 99% CL since in the data collected after the initial search, and up to end of August 2007, 8 out of 13 events were in correlation, while only 2.7 were expected on average from an isotropic distribution. It may be noted that the fact that the VC catalog is not complete nor uniform has absolutely
no relevance for the significance of this test. On the other hand, it is also important that the binomial probability scan performed does not test for an overall global proportionality across the sky between the events and a particular source model based on the AGN distribution, and hence the incompleteness of this catalog is not an obstacle to establish the presence of a correlation (eventually one could expect to just miss some correlations due to the catalog incompleteness, but not to enhance them). Another feature that has been pointed out in [8] is the apparent paucity of events from the region of the Virgo cluster (no events with E > 57 EeV fall within 20◦ of the location of M87 at (, b) = (−76.2◦ , 74.5◦ )). It has to be taken into account that Virgo is however in a comparatively low exposure region (with about 3 times smaller exposure than the Cen A region) and that being the Virgo cluster quite nearby, at less than 20 Mpc, a large fraction of the AGN cataloged in this region are quite faint, and are hence probably
E. Roulet / Nuclear Physics B (Proc. Suppl.) 190 (2009) 169–173
not particularly good candidate sites for UHECR acceleration. There are also many comparably faint AGN farther away which are below the sensitivity of the surveys and are hence not included in the VC catalog. It will be anyhow interesting to keep looking into the possible absence of events from Virgo with enlarged future data sets. In conclusion, the Auger Observatory has found a significant correlation between the arrival directions of the highest energy events, with E > 57 EeV, and the distribution of the nearby structures within ∼ 100 Mpc. This was established by correlating the events with the distribution of known AGN. This gives a strong support to the idea that above the ankle the CRs are of extragalactic origin. Moreover, it suggests that the observed attenuation in the CR spectrum above 40 EeV is indeed due to the GZK effect, and not just to the exhaustion of the acceleration power of the sources. This also suggests that we may be at the beginning of the era of charged particle astronomy. REFERENCES 1. The Pierre Auger Collaboration, Astropart. Phys. 29 (2008) 243-256 2. The Pierre Auger Collaboration, Phys. Rev. Lett. 100 (2008) 211101 3. R. U. Abbasi et al. (HiRes Collaboration), Phys. Rev. Lett. 100 (2008) 101101 4. The Pierre Auger Collaboration, Phys. Rev. Lett. 101 (2008) 061101 5. K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G. T. Zatsepin and V. A. Kuzmin, JETP Lett. 4 (1966) 78. 6. D. Harari, S. Mollerach, E. Roulet, JCAP 0611:012 (2006) 7. The Pierre Auger Collaboration, Science 318 (2007) 939-943 8. The Pierre Auger Collaboration, Astropart. Phys. 29 (2008) 188-204 9. S. Mollerach, for the Pierre Auger Collaboration, (2007) arxiv:0706.1749 [astro-ph]
173