Abstract
We discuss the GZK horizon of protons and present a method to constrain the injection spectrum of ultrahigh energy cosmic rays (UHECRs) from supposedly identified extragalactic sources. This method can be applied even when only one or two events per source are observed and is based on the analysis of the probability for a given source to populate different energy bins, depending on the actual cosmic ray injection spectral index. In particular, we show that for a typical source density of 4 × 10−5 Mpc−3, a data set of 100 events above 6 × 1019 eV allows one in 97% of all cases to distinguish a source spectrum dN/dE ∝ E −1.1 from one with E –2.7 at 95% confidence level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Kachelrieß and D. V. Semikoz, Astropart. Phys. 26, 10 (2006) [astro-ph/0512498].
S. Mollerach et al., in Proc. Mexico, 2007 (in press); arXiv:0706.1749 [astro-ph].
J. Abraham, P. Abreu, M. Aglietta, et al., Astropart. Phys. 29, 188 (2008); astro-ph/0712.2843.
R. U. Abbasi, T. Abu-Zayyad, M. Allen, et al. (HiRes Collab.), arXiv:0804.0382 [astro-ph]; D. S. Gorbunov, P. G. Tinyakov, I. I. Tkachev, et al., arXiv:0804.1088 [astro-ph]; I. V. Moskalenko, L. Stawarz, T. A. Porter, et al., arXiv:0805.1260 [astro-ph].
K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G. T. Zatsepin and V. A. Kuzmin, JETP Lett. 4, 78 (1966).
M. Kachelrieß, P. D. Serpico, and M. Teshima, Astropart. Phys. 26, 378 (2006); astro-ph/0510444.
M. Kachelrieß and D. V. Semikoz, Phys. Lett. B 634, 143 (2006); astro-ph/0510188.
V. S. Berezinskii, S. V. Bulanov, V. A. Dogiel, et al., Astrophysics of Cosmic Rays (North-Holland, Amsterdam, 1990); T. Gaisser, Cosmic Rays and Particle Physics (Cambridge Univ., Cambridge, 1991); R. J. Protheroe and R. W. Clay, Publ. Astron. Soc. Australia 21, 1 (2004); astro-ph/0311466.
A. Neronov and D. Semikoz, New Astronomy Rev. 47, 693 (2003), A. Neronov, D. Semikoz, and I. Tkachev, arXiv:0712.1737 [astro-ph].
A. Neronov, P. Tinyakov, and I. Tkachev, JETP 100, 656 (2005); astro-ph/0402132.
A. Neronov, D. Semikoz, F. Aharonian, and O. Kalashev, Phys. Rev. Lett. 89, 051101 (2002); astro-ph/0201410.
E. V. Derishev, F. A. Aharonian, V. V. Kocharovsky, et al., Phys. Rev. D 68, 043003 (2003); astro-ph/0301263.
V. V. Vlasov, S. K. Zhdanov, and B. A. Trubnikov, Fiz. Plasmy 16, 1457 (1990).
P. Blasi and D. de Marco, Astropart. Phys. 20, 559 (2004); astro-ph/0307067; M. Kachelrieß and D. Semikoz, Astropart. Phys. 23, 486 (2005); astro-ph/0405258.
A. Cuoco, S. Hannestad, T. Haugboelle, et al., Astrophys. J. 676, 807 (2008); 0709.2712 [astro-ph].
A. Mücke, R. Engel, J. P. Rachen, et al., Comput. Phys. Commun. 124, 290 (2000); astro-ph/9903478.
V. Berezinsky, A. Z. Gazizov, and S. I. Grigorieva, Phys. Rev. D 74, 043005 (2006); hep-ph/0204357.
See also [17] and V. Berezinsky, A. Gazizov, and M. Kachelrieß, Phys. Rev. Lett. 97, 231101 (2006); astro-ph/0612247.
D. Harari, S. Mollerach, and E. Roulet, JCAP 0611, 012 (2006); astro-ph/0609294.
O. E. Kalashev, B. A. Khrenov, P. Klimov, et al., arXiv:0710.1382 [astro-ph].
V. Berezinsky, A. Z. Gazizov, and S. I. Grigorieva, astroph/ 0210095; Phys. Lett. B 612, 147 (2005); astroph/0502550.
D. Allard, E. Parizot, and A. V. Olinto, Astropart. Phys. 27, 61 (2007); astro-ph/0512345.
M. Ave et al., in Proc. 30th International Cosmic Ray Conference, Mèrida, Mexico, 2007, p. 0297.
Author information
Authors and Affiliations
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Kachelrieß, M., Parizot, E. & Semikoz, D.V. The GZK horizon and constraints on the cosmic ray source spectrum from observations in the GZK regime. Jetp Lett. 88, 553–557 (2008). https://doi.org/10.1134/S0021364008210017
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364008210017