- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Optical depth of the Universe to ultrahigh energy cosmic ray scattering in the magnetized large scale structure

Kumiko Kotera* and Martin Lemoine†

  • Institut d’Astrophysique de Paris UMR7095 - CNRS, Université Pierre & Marie Curie, 98 bis boulevard Arago F-75014 Paris, France

  • *kotera@iap.fr
  • †lemoine@iap.fr
PDF

Phys. Rev. D 77, 123003 – Published 12 June, 2008

DOI: https://doi.org/10.1103/PhysRevD.77.123003

Abstract

This paper provides an analytical description of the transport of ultrahigh energy cosmic rays in an inhomogeneously magnetized intergalactic medium. The latter is modeled as a collection of magnetized scattering centers, such as radio cocoons, magnetized galactic winds, clusters or magnetized filaments of large scale structure, with negligible magnetic fields in between. Magnetic deflection is no longer a continuous process, it is rather dominated by scattering events. We study the interaction between high-energy cosmic rays and the scattering agents. We then compute the optical depth of the Universe to cosmic ray scattering and discuss the phenomenological consequences for various source scenarios. For typical parameters of the scattering centers, the optical depth is greater than unity at 5×1019  eV, but the total angular deflection is smaller than unity. One important consequence of this scenario is the possibility that the last scattering center encountered by a cosmic ray be mistaken with the source of this cosmic ray. In particular, we suggest that part of the correlation recently reported by the Pierre Auger Observatory may be affected by such delusion: this experiment may be observing in part the last scattering surface of ultrahigh energy cosmic rays rather than their source population. Since the optical depth falls rapidly with increasing energy, one should probe the arrival directions of the highest energy events beyond 1020  eV on an event by event basis to circumvent this effect.

View figure in article

Article Text

References (110)

  1. J. Abraham et al. (The Pierre Auger Collaboration), Science 318, 938 (2007).
  2. J. Abraham et al. (The Pierre Auger Collaboration) Astropart. Phys. 29,188 (2008).
  3. T. Stanev, P. L. Biermann, J. Lloyd-Evans, J. P. Rachen, and A. A. Watson, Phys. Rev. Lett. 75, 3056 (1995).
  4. P. G. Tinyakov and I. I. Tkachev, JETP Lett. 74, 445 (2001).
  5. D. S. Gorbunov, P. G. Tinyakov, I. I. Tkachev, and S. V. Troitsky, JETP Lett. 80, 145 (2004); Pisma Zh. Eksp. Teor. Fiz. 80, 167 (2004).
  6. P. G. Tinyakov and I. I. Tkachev, Phys. Rev. D 69, 128301 (2004).
  7. N. W. Evans, F. Ferrer, and S. Sarkar, Phys. Rev. D 69, 128302 (2004).
  8. R. U. Abbasi, T. Abu-Zayyad, J. F. Amann, G. Archbold, K. Belov, J. W. Belz, S. BenZvi, D. R. Bergman, S. A. Blake, and J. H. Boyer et al., Astrophys. J. 636, 680 (2006).
  9. Y. Uchihori, M. Nagano, M. Takeda, M. Teshima, J. Lloyd-Evans, and A. A. Watson, Astropart. Phys. 13, 151 (2000).
  10. G. R. Farrar, A. A. Berlind, and D. W. Hogg, Astrophys. J. Lett. 642, L89 (2006).
  11. R. U. Abbasi, T. Abu-Zayyad, J. F. Amann, G. Archbold, R. Atkins, J. A. Bellido, K. Belov, J. W. Belz, S. Y. Ben-Zvi, and D. R. Bergman et al., Astrophys. J. 623, 164 (2005).
  12. P. P. Kronberg, Rep. Prog. Phys. 57, 325 (1994).
  13. J. P. Vallée, Fundam. Cosm. Phys. 19, 1 (1997).
  14. E. Waxman and J. Miralda-Escudé, Astrophys. J. 472, L89 (1996).
  15. A. Achterberg, Y. A. Gallant, C. A. Norman, and D. B. Melrose, arXiv:astro-ph/9907060 [Astrophysics (Engl. Transl.) (to be published)].
  16. D. Harari, S. Mollerach, E. Roulet, and F. Sánchez, J. High Energy Phys. 3 (2002) 45.
  17. D. Harari, S. Mollerach, and E. Roulet, J. High Energy Phys. 7 (2002) 6.
  18. J. Wdowczyk and A. W. Wolfendale, Nature (London) 281, 356 (1979).
  19. V. S. Berezinskii, S. I. Grigor’eva, and V. A. Dogiel, Astron. Astrophys. 232, 582 (1990).
  20. P. Blasi and A. V. Olinto, Phys. Rev. D 59, 023001 (1998).
  21. R. Lampard, R. W. Clay, and B. R. Dawson, Astropart. Phys. 7, 213 (1997).
  22. G. A. Medina Tanco, E. M. de Gouveia dal Pino, and J. E. Horvath, Astropart. Phys. 6, 337 (1997).
  23. M. Lemoine, G. Sigl, A. Olinto, and D. N. Schramm, Astrophys. J. 486, L115 (1997).
  24. G. Sigl, M. Lemoine, and A. V. Olinto, Phys. Rev. D 56, 4470 (1997).
  25. R. W. Clay, S. Cook, B. R. Dawson, A. G. K. Smith, and R. Lampard, Astropart. Phys. 9, 221 (1998).
  26. T. Stanev, R. Engel, A. Mücke, R. J. Protheroe, and J. P. Rachen, Phys. Rev. D 62, 093005 (2000).
  27. H. Yoshiguchi, S. Nagataki, S.-y. Tsubaki, and K. Sato, Astrophys. J. 586, 1211 (2003).
  28. O. Deligny, A. Letessier-Selvon, and E. Parizot, Astropart. Phys. 21, 609 (2004).
  29. G. A. Medina Tanco, Astrophys. J. Lett. 505, L79 (1998).
  30. G. Sigl, M. Lemoine, and P. Biermann, Astropart. Phys. 10, 141 (1999).
  31. M. Lemoine, G. Sigl, and P. Biermann, arXiv:astro-ph/9903124.
  32. Y. Ide, S. Nagataki, S. Tsubaki, H. Yoshiguchi, and K. Sato, Publ. Astron. Soc. Jpn. 53, 1153 (2001).
  33. C. Isola, M. Lemoine, and G. Sigl, Phys. Rev. D 65, 023004 (2001).
  34. C. Isola and G. Sigl, Phys. Rev. D 66, 083002 (2002).
  35. T. Stanev, D. Seckel, and R. Engel, Phys. Rev. D 68, 103004 (2003).
  36. G. Sigl, F. Miniati, and T. A. Enßlin, Phys. Rev. D 68, 043002 (2003).
  37. G. Sigl, F. Miniati, and T. A. Enßlin, Phys. Rev. D 70, 043007 (2004).
  38. E. Armengaud, G. Sigl, and F. Miniati, Phys. Rev. D 72, 043009 (2005).
  39. K. Dolag, D. Grasso, V. Springel, and I. Tkachev, J. Korean Astron. Soc. 37, 427 (2004).
  40. K. Dolag, D. Grasso, V. Springel, and I. Tkachev, J. Cosmol. Astropart. Phys. 1 (2005) 9.
  41. H. Kang, S. Das, D. Ryu, and J. Cho, arXiv:0706.2597.
  42. G. Sigl, Phys. Rev. D 75, 103001 (2007).
  43. G. A. Medina Tanco, arXiv:astro-ph/9707054.
  44. H. Takami, H. Yoshiguchi, and K. Sato, Astrophys. J. 639, 803 (2006).
  45. H. Takami and K. Sato, arXiv:0706.3666.
  46. K. Kotera and M. Lemoine, Phys. Rev. D 77, 023005 (2008).
  47. G. Medina-Tanco and T. A. Enßlin, Astropart. Phys. 16, 47 (2001).
  48. V. Berezinsky, A. Z. Gazizov, and S. I. Grigorieva, arXiv:astro-ph/0210095.
  49. L. M. Widrow, Rev. Mod. Phys. 74, 775 (2002).
  50. D. Ryu, H. Kang, and P. L. Biermann, Astron. Astrophys. 335, 19 (1998).
  51. G. Sigl, F. Miniati, and T. A. Enßlin, Phys. Rev. D 70, 043007 (2004).
  52. K. Dolag, Astron. Nachr. 327, 575 (2006).
  53. P. P. Kronberg, H. Lesch, and U. Hopp, Astrophys. J. 511, 56 (1999).
  54. G. T. Birk, H. Wiechen, H. Lesch, and P. P. Kronberg, Astron. Astrophys. 353, 108 (2000).
  55. S. Bertone, C. Vogt, and T. Enßlin, Mon. Not. R. Astron. Soc. 370, 319 (2006).
  56. M. J. Rees and G. Setti, Nature (London) 219, 127 (1968).
  57. S. R. Furlanetto and A. Loeb, Astrophys. J. 556, 619 (2001).
  58. Gopal-Krishna and P. J. Wiita, Astrophys. J. Lett. 560, L115 (2001).
  59. S. Bertone, F. Stoehr, and S. D. M. White, Mon. Not. R. Astron. Soc. 359, 1201 (2005).
  60. P. P. Kronberg, Q. W. Dufton, H. Li, and S. A. Colgate, Astrophys. J. 560, 178 (2001).
  61. L. Ferrarese and H. Ford, Space Sci. Rev. 116, 523 (2005).
  62. T. R. Lauer, S. M. Faber, D. Richstone, K. Gebhardt, S. Tremaine, M. Postman, A. Dressler, M. C. Aller, A. V. Filippenko, and R. Green et al., Astrophys. J. 662, 808 (2007).
  63. E. R. Seaquist and N. Odegard, Astrophys. J. 369, 320 (1991).
  64. M. Pettini, S. A. Rix, C. C. Steidel, K. L. Adelberger, M. P. Hunt, and A. E. Shapley, Astrophys. J. 569, 742 (2002).
  65. K. L. Adelberger, C. C. Steidel, A. E. Shapley, and M. Pettini, Astrophys. J. 584, 45 (2003).
  66. T. M. Heckman, in Gas and Galaxy Evolution, Astronomical Society of the Pacific Conference Series Vol. 240, edited by J. E. Hibbard, M. Rupen, and J. H. van Gorkom, (Astronomical Society of the Pacific, San Francisco, 2001), p. 345.
  67. A. Aguirre, L. Hernquist, J. Schaye, D. H. Weinberg, N. Katz, and J. Gardner, Astrophys. J. 560, 599 (2001).
  68. R. Cen, K. Nagamine, and J. P. Ostriker, Astrophys. J. 635, 86 (2005).
  69. E. Scannapieco, C. Pichon, B. Aracil, P. Petitjean, R. J. Thacker, D. Pogosyan, J. Bergeron, and H. M. P. Couchman, Mon. Not. R. Astron. Soc. 365, 615 (2006).
  70. H.-P. Reuter, U. Klein, H. Lesch, R. Wielebinski, and P. P. Kronberg, Astron. Astrophys. 256, 10 (1992).
  71. T. E. Clarke, P. P. Kronberg, and H. Böhringer, Astrophys. J. Lett. 547, L111 (2001).
  72. F. Govoni, M. Murgia, L. Feretti, G. Giovannini, K. Dolag, and G. B. Taylor, Astron. Astrophys. 460, 425 (2006).
  73. M. Brüggen, M. Ruszkowski, A. Simionescu, M. Hoeft, and C. Dalla Vecchia, Astrophys. J. Lett. 631, L21 (2005).
  74. A. G. Doroshkevich, D. L. Tucker, R. Fong, V. Turchaninov, and H. Lin, Mon. Not. R. Astron. Soc. 322, 369 (2001).
  75. F. Miniati, D. Ryu, H. Kang, T. W. Jones, R. Cen, and J. P. Ostriker, Astrophys. J. 542, 608 (2000).
  76. H. Kang, D. Ryu, R. Cen, and D. Song, Astrophys. J. 620, 21 (2005).
  77. R. M. Kulsrud, R. Cen, J. P. Ostriker, and D. Ryu, Astrophys. J. 480, 481 (1997).
  78. A. Loeb and E. Waxman, Nature (London) 405, 156 (2000).
  79. F. Miniati, Mon. Not. R. Astron. Soc. 337, 199 (2002).
  80. U. Keshet, E. Waxman, A. Loeb, V. Springel, and L. Hernquist, Astrophys. J. 585, 128 (2003).
  81. J. Vink and J. M. Laming, Astrophys. J. 584, 758 (2003).
  82. E. G. Berezhko, L. T. Ksenofontov, and H. J. Völk, Astron. Astrophys. 412, L11 (2003).
  83. K. Greisen, Phys. Rev. Lett. 16, 748 (1966).
  84. G. T. Zatsepin and V. A. Kuzmin, JETP Lett. 4, 78 (1966).
  85. R. Teyssier, Astron. Astrophys. 385, 337 (2002).
  86. E. Waxman, Phys. Rev. Lett. 75, 386 (1995).
  87. J. Alvarez-Muñiz, R. Engel, and T. Stanev, Astrophys. J. 572, 185 (2002).
  88. H. Takami and K. Sato, arXiv:0711.2386.
  89. C. Alcock and S. Hatchett, Astrophys. J. 222, 456 (1978).
  90. G. Sigl, M. Lemoine, and P. Biermann, Astropart. Phys. 10, 141 (1999).
  91. E. Waxman, in Physics and Astrophysics of Ultra-High-Energy Cosmic Rays, edited by M. Lemoine and G. Sigl, Lecture Notes in Physics Vol. 576 (Springer Verlag, Berlin, 2001), p. 122.
  92. W. Saunders, W. J. Sutherland, S. J. Maddox, O. Keeble, S. J. Oliver, M. Rowan-Robinson, R. G. McMahon, G. P. Efstathiou, H. Tadros, and S. D. M. White et al., Mon. Not. R. Astron. Soc. 317, 55 (2000).
  93. K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann, Astrophys. J. 622, 759 (2005).
  94. D. Harari, S. Mollerach, and E. Roulet, J. High Energy Phys. 8 (1999) 22.
  95. R. Aloisio and V. Berezinsky, Astrophys. J. 612, 900 (2004).
  96. V. Berezinsky and A. Gazizov, Astrophys. J. 643, 8 (2006).
  97. M. Lemoine, Phys. Rev. D 71, 083007 (2005).
  98. R. Aloisio and V. Berezinsky, Astrophys. J. 625, 249 (2005).
  99. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
  100. R. C. Ball, S. Havlin, and G. H. Weiss, J. Phys. A 20, 4055 (1987).
  101. C. A. Norman, D. B. Melrose, and A. Achterberg, Astrophys. J. 454, 60 (1995).
  102. F. Casse, M. Lemoine, and G. Pelletier, Phys. Rev. D 65, 023002 (2001).
  103. D. Gorbunov, P. Tinyakov, I. Tkachev, and S. Troitsky, arXiv:0711.4060.
  104. E. Waxman, K. B. Fisher, and T. Piran, Astrophys. J. 483, 1 (1997).
  105. V. Berezinsky, A. Gazizov, and S. Grigorieva, Phys. Rev. D 74, 043005 (2006).
  106. D. Harari, S. Mollerach, and E. Roulet, J. Cosmol. Astropart. Phys. 11 (2006) 12.
  107. A. Cuoco, R. D’Abrusco, G. Longo, G. Miele, and P. D. Serpico, J. Cosmol. Astropart. Phys. 1 (2006) 9.
  108. Pierre Auger North Observatory, http://www.augernorth.org.
  109. J. Giacalone and J. R. Jokipii, Astrophys. J. 520, 204 (1999).
  110. J. Candia and E. Roulet, J. Cosmol. Astropart. Phys. 10 (2004) 007.

Outline

Information

Phys. Rev. D 77, 123003– Published 12 June, 2008
  • Received 17 January 2008

© 2008 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation