- Email: [email protected]
EleCa: A Monte Carlo code for the propagation of extragalactic photons at ultra-high energy
Available online at www.sciencedirect.com
Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282 www.elsevier.com/locate/npbps
EleCa: a Monte Carlo code for the propagation of extragalactic photons at ultra-high energy Mariangela Settimoa , Manlio De Domenicob,1 , Haris Lyberisc b Laboratory
a University of Siegen, Germany of Complex Systems, Scuola Superiore di Catania and INFN, Italy c Federal University of Rio de Janeiro, Brazil
Abstract Ultra high energy photons, above 1017 -1018 eV, can interact with the extragalactic background radiation leading to the development of electromagnetic cascades. A Monte Carlo code to simulate the electromagnetic cascades initiated by high-energy photons and electrons is presented. Results from simulations and their impact on the predicted flux at Earth are discussed in different astrophysical scenarios. Keywords: UHE photons, extragalactic propagation, electromagnetic cascades
1. Introduction Ultra-high energy (UHE) photons are expected to be produced in the interactions of UHE cosmic rays with matter, e.g. with gas around a source, or with the extragalactic background radiation (EBR). In particular, photons can be created from the decay of neutral pions produced in the interaction of UHE nuclei with the EBR photons, for instance, because of the Greisen-ZatsepinKuz’min (GZK) effect [1, 2]. Recent measurements of the UHECR energy spectrum [3, 4] have confirmed a flux suppression above 50 EeV (1 EeV = 1018 eV) compatible with the expectation from GZK effect, even if other alternatives (e.g., a physical limit to the maximum acceleration at the source) can not be ruled out. Hence, the observation of UHE photons would be an independent evidence for the existence of the GZK effect, providing hints on the nature of UHECR, on astrophysical sources and on environmental conditions. A large fraction of UHE photons are also expected, from the decay or the annihilation of supermassive particles [5], in some exotic (top-down) models for UHECR acceleration. No UHE photons have been observed so far and 1 Now
at School of Computer Science, University of Birmingham,
UK
0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.05.045
upper limits to the their flux have been placed [6, 7], partly disfavoring exotic models. Moreover, the current experiments are reaching the sensitivity to explore the region of expected GZK photons in the most optimistic scenarios, thus motivating further study with detailed simulations of photons and nuclei propagation. During their propagation, photons can produce electrons and positrons which can subsequently undergo new interactions producing upscattered photons. In this proceeding, we present EleCa, a full Monte Carlo code for the development of these Electromagnetic Cascades. The details of the interaction processes and of the developed code are given in section 2. As shown in section 3, a prediction of the expected GZK photon flux at Earth can be derived by EleCa used in combination with an external code propagating UHE nuclei in a wide variety of astrophysical scenarios. 2. Propagation of photons and the EleCa simulator EleCa is a C++ code developed with high modularity, thus easily integrable with existing codes for the propagation of UHE nuclei. It simulates the propagation of electromagnetic particles (γ, e+ and e− ). The
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Figure 2: Different parameterizations of extragalactic background radiation (EBR) as a function of relic photon energy. The red solid line indicates the EBR parameterization included in this study.
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Figure 1: Mean interaction lengths for photons (top) and electrons/positrons (bottom) for the total EBR (solid). Dashed lines are given for each individual contributions to the radiation background (see text). The interaction length corresponding to the adiabatic and synchrotron energy losses are also shown as a dot-dashed and dotted lines respectively.
dominant interaction process for photons is the Pair Production (PP), γγb → e+ e− , where γb is the background photon. Another process, the Double Pair Production (DPP), γγb → e+ e− e+ e− , dominates at energies above 100 EeV and is currently not implemented in the code. The interaction lengths derived for PP, at the present epoch (z = 0), are shown in Fig. 1 (top) for the total range of background photons (solid line) and for the single components (dashed lines) of background radiation: Optical (Opt), Far, High and Low Infrared (CIRB), Cosmic Microwave (CMB) (see [8] and references herein) and Universal Radio (URB) [9]. The EBR used for this study is shown in the top panel of Fig. 2. From
Fig. 1 it is evident that the Universe is opaque to photons with energy of a few hundreds or thousands TeV, getting more transparent at lower energies, where photons mainly interact with the IR background, and in the EeV energy range, where the interaction with URB becomes the dominant process. Previous results [10, 11] are also shown for comparison: the observed differences are due to the different models assumed for the IRB and URB. Electrons are cooled down via the Inverse Compton Scattering (ICS), eγb → eγ, or absorbed through the Triplet Pair Production (TPP), eγb → ee+ e− . The interaction lengths of the two processes are shown in Fig. 1 (bottom) for the whole EBR and for each background component separately, and together with previous results. The energy losses due to the adiabatic expansion of the Universe and to an average synchrotron radiation emissions by e+ /e− [12] are included and treated as continuous loss processes. The interaction lengths corresponding to the synchrotron emission for three different intensities of the magnetic field are shown in Fig. 1 (bottom). Deflections due to the extragalactic magnetic field are taken into account by assuming the “small angle” approximation [13], which is valid for magnetic fields with strength smaller than a few nG at the energy scale of interest for this study. Apart for the synchrotron emission, all the interactions are treated as stochastic processes in EleCa, which is in contrast to the existing simulators publicly available to the community [14, 15]. The simulation is performed through a Monte Carlo approach, where the energy of primary particles and secondary products are estimated according to the cross section dσ/dE corresponding to each process.
M. Settimo et al. / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282
Figure 3: Expected all-particles energy spectra obtained from HERMES for different astrophysical scenarios (see text).
3. Prediction of GZK photon fluxes at Earth UHE cosmic rays lose energy during their propagation from the sources to Earth. We simulate nuclei propagating in the Universe by means of HERMES [8], a novel Monte Carlo modular C++ code developed to follow the evolution of primary particles and their secondary products. HERMES allows the simulation of intervening magnetic fields, both extra-galactic (turbulent component) and galactic (several models for the regular component together with an additional turbulent one). The relevant energy losses are also included and all particles experience continuous adiabatic loss due to the expansion of the Universe. Moreover, the propagation of UHECRs is affected by their interactions with photons of the EBR (modeled as in Fig. 2). Such interactions are responsible for the (i) production of pairs of secondary e+ and e− ; (ii) photo-pion production, with pions decaying to secondary photons and neutrinos; (iii) photo-disintegration of nuclei, with A ≥ 2, into lighter nuclei. While process (i) is treated as a continuous energy loss, the simulation of processes (ii) and (iii) requires a full Monte Carlo approach, in order to properly take into account their stochastic nature. Different models, based on theoretical arguments or ad hoc Monte Carlo simulators, can be adopted for the cross-sections of these three processes. For further details about the available models we refer to [8]. For the present study, we use cross-sections provided by the TALYS [16] nuclear reaction code2 . The distribution of sources, their intrinsic luminosity, injection spectrum and evolution are tunable parameters 2 Update:
2011. Website: http://www.talys.eu/home/
281
in HERMES, allowing to simulate a wide variety of astrophysical scenarios and to investigate the impact of propagation on physical observable as the flux, or the chemical composition observed at Earth. An example of the predicted all-particles spectra obtained with HERMES, for different astrophysical scenarios, is shown in Fig. 3. In particular, we consider sources homogeneously distributed up to zmax = 1.5, power-law injection spectrum with varying spectral index, different mass composition (protons and irons) and different source evolution, following the star formation rate (SFR) or active galactic nuclei (AGN). The observed fluxes of UHECRs reported by HiRes [3] and the Pierre Auger Observatory [4] are shown for comparison. UHE photons produced by HERMES as products of nuclei interactions, are propagated through the EleCa code. For this study, we assume uniformly distributed sources injecting proton (red) and iron nuclei (blue) according to a power-law spectrum up to a maximum energy Emax = Z × 1021 eV. In Fig. 4 (top), we show the photon fluxes expected at Earth for three different spectral (γ = -2.0, -2.3 and -2.7) of the injected nuclear spectrum at the source. In the bottom panel, the impact of the source distance is shown, by plotting the expected fluxes from sources with spectral index γ = 2.0 and Emax = Z × 1021 eV. In both cases, a Kolmogorov-like extragalactic magnetic field with rms strength of 0.1 nG is considered. Given the “small angle approximation” currently used in the code for the treatment of the deflection in the magnetic field, only secondary electromagnetic particles above 1016 eV are followed. 4. Outlook The EleCa code for the simulation of the development of electromagnetic cascades initiated by UHE photons and e+ /e− is presented in this proceeding. It’s a Monte Carlo code that can be easily combined with external codes for the propagation of UHE nuclei (here HERMES) thanks to its C++ modular framework. This allows us to predict the GZK photon fluxes expected at Earth in different scenarios. Preliminary results are shown in the energy range above 1016.5 eV. The predicted fluxes at Earth can differ by several orders of magnitude depending on the chosen enviromental configurations (EBR, magnetic fields), source distribution and spectra, and chemical composition. The theoretical prediction of photon fluxes, combined with the experimental observations (or non-observations) of UHE photons can help to constrain the phase-space of these parameters. Further improvements, as the implementation of the Double Pair Production (DPP), a 3D version
282
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M. Settimo et al. / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282
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Emax = Z x 10 eV B = 0.1 nG z max = 0.1
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Figure 4: Top: photon fluxes expected at Earth from sources injecting proton (red) and iron (blue) nuclei with spectrum E−2 , E−2.3 and E−2.7 , Emax = Z × 1021 eV, with a Kolmogorov-like extragalactic magnetic field with strength of 0.1 nG. Bottom: as in the upper panel, but for sources uniformly distributed in three different ranges of distances (4400 Mpc, 10-400 Mpc and 100-400 Mpc) and with a flux E −2 .
with a more realistic treatment of extragalactic magnetic fields, new environment models (e.g. URB, extragalactic medium) and optimization for the propagation of photons at the TeV scale are in progress. Acknowledgments The authors are grateful to Markus Risse for useful discussions. M.S. acknowledges support by the BMBF Verbundforschung Astroteilchenphysik and by the Helmholtz Alliance for Astroparticle Physics (HAP). References [1] K. Greisen, End to the cosmic ray spectrum?, Phys.Rev.Lett. 16 (1966) 748–750. [2] G. Zatsepin, V. Kuzmin, Upper limit of the spectrum of cosmic rays, JETP Lett. 4 (1966) 78–80.
[3] B. Zhang, Z. Cao, The measurement of UHECR spectrum with the HiRes experiment in stereo mode, Nucl.Phys.Proc.Suppl. 175-176 (2008) 241–244. [4] P. Abreu, et al., Measurement of the Cosmic Ray Energy Spectrum Using Hybrid Events of the Pierre Auger Observatory, Eur.Phys.J.Plus 127 (2012) 87. arXiv:1208.6574. [5] G. Gelmini, O. E. Kalashev, D. V. Semikoz, GZK Photons in the Minimal Ultrahigh Energy Cosmic Rays Model, Astropart.Phys. 28 (2007) 390–396. arXiv:astro-ph/0702464. [6] M. Settimo, An update on a search for ultra-high energy photons using the Pierre Auger Observatory, Proceedings of 32nd ICRC, Beijing 2 (2011) 51. arXiv:1107.4805. [7] G. Rubtsov, Proceedings of 32nd ICRC, Beijing. [8] M. D. Domenico, Propagation of ultra-high energy cosmic rays and anisotropy studies with the pierre auger observatory: the multiscale approach, Ph.D. thesis (2011). URL http://dspace.unict.it/handle/10761/992 [9] R. J. Protheroe, P. L. Biermann, A new estimate of the extragalactic radio background and implications for ultra-highenergy gamma ray propagation, Astropart. Phys. 6 (1996) 45– 54. URL http://fr.arxiv.org/abs/astro-ph/9605119 [10] S. Lee, On the propagation of extragalactic high-energy cosmic and gamma-rays, Phys. Rev. D58 (1998) 043004. URL http://fr.arxiv.org/abs/astro-ph/9604098 [11] R. J. Protheroe, Effect of electron-photon cascading on the observed energy spectra of extragalactic sources of ultra-highenergy gamma-rays, MNRAS 221 (1986) 769–788. [12] T. Stanev, High energy cosmic rays; 2nd ed., Springer-Praxis books in astrophysics and astronomy, Springer, Berlin, 2004. [13] D. Hooper, S. Sarkar, A. M. Taylor, The intergalactic propagation of ultrahigh energy cosmic ray nuclei, Astropart.Phys. 27 (2007) 199–212. arXiv:astro-ph/0608085. [14] E. Armengaud, G. Sigl, T. Beau, F. Miniati, Crpropa: A numerical tool for the propagation of uhe cosmic rays, gamma-rays and neutrinos. URL http://fr.arxiv.org/abs/astro-ph/0603675 [15] M. Kachelriess, S. Ostapchenko, R. Tomas, ELMAG: A Monte Carlo simulation of electromagnetic cascades on the extragalactic background light and in magnetic fields, Comput.Phys.Commun. 183 (2012) 1036–1043. arXiv:1106.5508. [16] A. Koning, S. Hilaire, M. Duijvestijn, Talys: Comprehensive nuclear reaction modeling, in: R. Haight, M. Chadwick, T. Kawano, , P. Talou (Eds.), Proc. Intern. Conf. Nucl. Data for Sci. Techn., Vol. 769, 2005, pp. 1154–1159. [17] J. Abraham, et al., Upper limit on the cosmic-ray photon fraction at EeV energies from the Pierre Auger Observatory, Astropart.Phys. 31 (2009) 399–406. arXiv:0903.1127. [18] Talys official website, http://www.talys.eu/home/ (Aug. 2011).
Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282 www.elsevier.com/locate/npbps
EleCa: a Monte Carlo code for the propagation of extragalactic photons at ultra-high energy Mariangela Settimoa , Manlio De Domenicob,1 , Haris Lyberisc b Laboratory
a University of Siegen, Germany of Complex Systems, Scuola Superiore di Catania and INFN, Italy c Federal University of Rio de Janeiro, Brazil
Abstract Ultra high energy photons, above 1017 -1018 eV, can interact with the extragalactic background radiation leading to the development of electromagnetic cascades. A Monte Carlo code to simulate the electromagnetic cascades initiated by high-energy photons and electrons is presented. Results from simulations and their impact on the predicted flux at Earth are discussed in different astrophysical scenarios. Keywords: UHE photons, extragalactic propagation, electromagnetic cascades
1. Introduction Ultra-high energy (UHE) photons are expected to be produced in the interactions of UHE cosmic rays with matter, e.g. with gas around a source, or with the extragalactic background radiation (EBR). In particular, photons can be created from the decay of neutral pions produced in the interaction of UHE nuclei with the EBR photons, for instance, because of the Greisen-ZatsepinKuz’min (GZK) effect [1, 2]. Recent measurements of the UHECR energy spectrum [3, 4] have confirmed a flux suppression above 50 EeV (1 EeV = 1018 eV) compatible with the expectation from GZK effect, even if other alternatives (e.g., a physical limit to the maximum acceleration at the source) can not be ruled out. Hence, the observation of UHE photons would be an independent evidence for the existence of the GZK effect, providing hints on the nature of UHECR, on astrophysical sources and on environmental conditions. A large fraction of UHE photons are also expected, from the decay or the annihilation of supermassive particles [5], in some exotic (top-down) models for UHECR acceleration. No UHE photons have been observed so far and 1 Now
at School of Computer Science, University of Birmingham,
UK
0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.05.045
upper limits to the their flux have been placed [6, 7], partly disfavoring exotic models. Moreover, the current experiments are reaching the sensitivity to explore the region of expected GZK photons in the most optimistic scenarios, thus motivating further study with detailed simulations of photons and nuclei propagation. During their propagation, photons can produce electrons and positrons which can subsequently undergo new interactions producing upscattered photons. In this proceeding, we present EleCa, a full Monte Carlo code for the development of these Electromagnetic Cascades. The details of the interaction processes and of the developed code are given in section 2. As shown in section 3, a prediction of the expected GZK photon flux at Earth can be derived by EleCa used in combination with an external code propagating UHE nuclei in a wide variety of astrophysical scenarios. 2. Propagation of photons and the EleCa simulator EleCa is a C++ code developed with high modularity, thus easily integrable with existing codes for the propagation of UHE nuclei. It simulates the propagation of electromagnetic particles (γ, e+ and e− ). The
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M. Settimo et al. / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282
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Figure 2: Different parameterizations of extragalactic background radiation (EBR) as a function of relic photon energy. The red solid line indicates the EBR parameterization included in this study.
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Figure 1: Mean interaction lengths for photons (top) and electrons/positrons (bottom) for the total EBR (solid). Dashed lines are given for each individual contributions to the radiation background (see text). The interaction length corresponding to the adiabatic and synchrotron energy losses are also shown as a dot-dashed and dotted lines respectively.
dominant interaction process for photons is the Pair Production (PP), γγb → e+ e− , where γb is the background photon. Another process, the Double Pair Production (DPP), γγb → e+ e− e+ e− , dominates at energies above 100 EeV and is currently not implemented in the code. The interaction lengths derived for PP, at the present epoch (z = 0), are shown in Fig. 1 (top) for the total range of background photons (solid line) and for the single components (dashed lines) of background radiation: Optical (Opt), Far, High and Low Infrared (CIRB), Cosmic Microwave (CMB) (see [8] and references herein) and Universal Radio (URB) [9]. The EBR used for this study is shown in the top panel of Fig. 2. From
Fig. 1 it is evident that the Universe is opaque to photons with energy of a few hundreds or thousands TeV, getting more transparent at lower energies, where photons mainly interact with the IR background, and in the EeV energy range, where the interaction with URB becomes the dominant process. Previous results [10, 11] are also shown for comparison: the observed differences are due to the different models assumed for the IRB and URB. Electrons are cooled down via the Inverse Compton Scattering (ICS), eγb → eγ, or absorbed through the Triplet Pair Production (TPP), eγb → ee+ e− . The interaction lengths of the two processes are shown in Fig. 1 (bottom) for the whole EBR and for each background component separately, and together with previous results. The energy losses due to the adiabatic expansion of the Universe and to an average synchrotron radiation emissions by e+ /e− [12] are included and treated as continuous loss processes. The interaction lengths corresponding to the synchrotron emission for three different intensities of the magnetic field are shown in Fig. 1 (bottom). Deflections due to the extragalactic magnetic field are taken into account by assuming the “small angle” approximation [13], which is valid for magnetic fields with strength smaller than a few nG at the energy scale of interest for this study. Apart for the synchrotron emission, all the interactions are treated as stochastic processes in EleCa, which is in contrast to the existing simulators publicly available to the community [14, 15]. The simulation is performed through a Monte Carlo approach, where the energy of primary particles and secondary products are estimated according to the cross section dσ/dE corresponding to each process.
M. Settimo et al. / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282
Figure 3: Expected all-particles energy spectra obtained from HERMES for different astrophysical scenarios (see text).
3. Prediction of GZK photon fluxes at Earth UHE cosmic rays lose energy during their propagation from the sources to Earth. We simulate nuclei propagating in the Universe by means of HERMES [8], a novel Monte Carlo modular C++ code developed to follow the evolution of primary particles and their secondary products. HERMES allows the simulation of intervening magnetic fields, both extra-galactic (turbulent component) and galactic (several models for the regular component together with an additional turbulent one). The relevant energy losses are also included and all particles experience continuous adiabatic loss due to the expansion of the Universe. Moreover, the propagation of UHECRs is affected by their interactions with photons of the EBR (modeled as in Fig. 2). Such interactions are responsible for the (i) production of pairs of secondary e+ and e− ; (ii) photo-pion production, with pions decaying to secondary photons and neutrinos; (iii) photo-disintegration of nuclei, with A ≥ 2, into lighter nuclei. While process (i) is treated as a continuous energy loss, the simulation of processes (ii) and (iii) requires a full Monte Carlo approach, in order to properly take into account their stochastic nature. Different models, based on theoretical arguments or ad hoc Monte Carlo simulators, can be adopted for the cross-sections of these three processes. For further details about the available models we refer to [8]. For the present study, we use cross-sections provided by the TALYS [16] nuclear reaction code2 . The distribution of sources, their intrinsic luminosity, injection spectrum and evolution are tunable parameters 2 Update:
2011. Website: http://www.talys.eu/home/
281
in HERMES, allowing to simulate a wide variety of astrophysical scenarios and to investigate the impact of propagation on physical observable as the flux, or the chemical composition observed at Earth. An example of the predicted all-particles spectra obtained with HERMES, for different astrophysical scenarios, is shown in Fig. 3. In particular, we consider sources homogeneously distributed up to zmax = 1.5, power-law injection spectrum with varying spectral index, different mass composition (protons and irons) and different source evolution, following the star formation rate (SFR) or active galactic nuclei (AGN). The observed fluxes of UHECRs reported by HiRes [3] and the Pierre Auger Observatory [4] are shown for comparison. UHE photons produced by HERMES as products of nuclei interactions, are propagated through the EleCa code. For this study, we assume uniformly distributed sources injecting proton (red) and iron nuclei (blue) according to a power-law spectrum up to a maximum energy Emax = Z × 1021 eV. In Fig. 4 (top), we show the photon fluxes expected at Earth for three different spectral (γ = -2.0, -2.3 and -2.7) of the injected nuclear spectrum at the source. In the bottom panel, the impact of the source distance is shown, by plotting the expected fluxes from sources with spectral index γ = 2.0 and Emax = Z × 1021 eV. In both cases, a Kolmogorov-like extragalactic magnetic field with rms strength of 0.1 nG is considered. Given the “small angle approximation” currently used in the code for the treatment of the deflection in the magnetic field, only secondary electromagnetic particles above 1016 eV are followed. 4. Outlook The EleCa code for the simulation of the development of electromagnetic cascades initiated by UHE photons and e+ /e− is presented in this proceeding. It’s a Monte Carlo code that can be easily combined with external codes for the propagation of UHE nuclei (here HERMES) thanks to its C++ modular framework. This allows us to predict the GZK photon fluxes expected at Earth in different scenarios. Preliminary results are shown in the energy range above 1016.5 eV. The predicted fluxes at Earth can differ by several orders of magnitude depending on the chosen enviromental configurations (EBR, magnetic fields), source distribution and spectra, and chemical composition. The theoretical prediction of photon fluxes, combined with the experimental observations (or non-observations) of UHE photons can help to constrain the phase-space of these parameters. Further improvements, as the implementation of the Double Pair Production (DPP), a 3D version
282
E2 J(E) [arbitrary units]
M. Settimo et al. / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 279–282
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Emax = Z x 10 eV B = 0.1 nG z max = 0.1
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Figure 4: Top: photon fluxes expected at Earth from sources injecting proton (red) and iron (blue) nuclei with spectrum E−2 , E−2.3 and E−2.7 , Emax = Z × 1021 eV, with a Kolmogorov-like extragalactic magnetic field with strength of 0.1 nG. Bottom: as in the upper panel, but for sources uniformly distributed in three different ranges of distances (4400 Mpc, 10-400 Mpc and 100-400 Mpc) and with a flux E −2 .
with a more realistic treatment of extragalactic magnetic fields, new environment models (e.g. URB, extragalactic medium) and optimization for the propagation of photons at the TeV scale are in progress. Acknowledgments The authors are grateful to Markus Risse for useful discussions. M.S. acknowledges support by the BMBF Verbundforschung Astroteilchenphysik and by the Helmholtz Alliance for Astroparticle Physics (HAP). References [1] K. Greisen, End to the cosmic ray spectrum?, Phys.Rev.Lett. 16 (1966) 748–750. [2] G. Zatsepin, V. Kuzmin, Upper limit of the spectrum of cosmic rays, JETP Lett. 4 (1966) 78–80.
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