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The end of the galactic cosmic ray energy spectrum – a phenomenological view

direct. indirect. knee. 2nd knee. Nagano & Watson, Rev. Mod. Phys. 72 (2000) 689. The end of the galactic cosmic ray energy spectrum – a phenomenological view. x 92. Jörg R. Hörandel University of Karlsruhe. Workshop on the Physics of the End of the Galactic Cosmic Ray Spectrum

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The end of the galactic cosmic ray energy spectrum – a phenomenological view

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  1. direct indirect knee 2nd knee Nagano & Watson, Rev. Mod. Phys. 72 (2000) 689 The end of the galactic cosmic ray energy spectrum – a phenomenological view x 92 Jörg R. Hörandel University of Karlsruhe Workshop on the Physics of the End of the Galactic Cosmic Ray Spectrum Aspen, April 25th – 30th, 2005

  2. Results from direct measurements (Z=1-28) protons Extrapolate power law spectra to high energies iron JRH, Astropart. Phys 19 (2003) 193

  3. Shape of energy spectrum Escape Leakage from Galaxy Escape Leakage from Galaxy fragmentation s ~ A2/3

  4. The poly-gonato model at low energies: solar modulation above Z*10 GeV: power laws with cut-off above knee: common gc above knee: common Dg rigidity dependent cut-off energy mass dependent constant • Parametrization of directly measured energy spectra for individual elements (Z=1-92) • Extrapolation to high energies and comparison to all-particle spectrum from EAS measurements link direct and indirect measurements JRH, Astropart. Phys 19 (2003) 193

  5. Elements heavier than iron (Z=29-92) abundance at ~1 GeV/n spectral index vs nuclear charge A = 2.70 +/- 0.19 B = (-8.34 +/- 4.67) 10-4 C = 1.51 +/- 0.13 JRH, Astropart. Phys 19 (2003) 193

  6. Cosmic-ray energy spectrum renormalizeenergy scale JRH, Astropart. Phys 19 (2003) 193

  7. Fit to the all-particle spectrum with rigidity dependent cut-off common Dg Ep [PeV] 4.49 +- 0.51 Ep [PeV] 4.51 +- 0.52 Dg 2.10 +- 0.24 gc -4.68 +- 0.23 ec 1.90 +- 0.19 ec 1.87 +- 0.18 c2/dof 0.113 c2/dof 0.116 common gc

  8. Fit result compared to indirect measurements

  9. Diffusion Model transport equation particle concentration transverse diffusion coefficient source term hall diffusion coefficient large halo model with antisymmetric regular magnetic field V.S. Ptuskin et al., A&A 268 (1993) 726

  10. Propagation of cosmic rays through Galaxy Diffusion model V.S. Ptuskin et al., A&A 268 (1993) 726 N.N. Kalmykov, A.I. Pavlov, 26th ICRC 4 (1999) 263 proton JRH, Kalmykov, Timokhin

  11. Propagation pathlength in Galaxy diffusion model JRH, Kalmykov, Timokhin

  12. Ratio of secondary to primary nuclei ACE/CRIS Leaky box model N. E. Yanasak, ApJ 563 (2001) 768

  13. Propagation pathlength in Galaxy 8 kpc * 1 p/cm3 l~E-0.2 diffusion model leaky box model residual pathlength model N. E. Yanasak, ApJ 563 (2001) 768 S.P. Swordy, 24th ICRC, Rome 2 (1995) 697

  14. Anisotropy amplitude vs energy Rayleigh vector V.S. Ptuskin, Adv. Space Res. 19 (1997) 697 J. Candia et al., J. Cosmol. Astropart. Phys. 5 (2003) 3 T. Antoni et al, ApJ 604 (2004) 687

  15. Age of cosmic rays ACE/CRIS 15*106 a t~E-0.05 diffusion model N. E. Yanasak, ApJ 563 (2001) 768 JRH, Kalmykov, Timokhin

  16. Shape of energy spectrum fragmentation s ~ A2/3 Escape Leakage from Galaxy

  17. Fraction of surviving nuclei during propagation Fraction of surviving nuclei QGSJET >~50% of nuclei survive without interaction Matter traversed by protons heavy nuclei  E~Z + cross sections from QGSJET JRH, Kalmykov, Timokhin

  18. Cosmic-ray energy spectrum ? according to Astropart. Phys. 19 (2003) 193

  19. knee 2nd knee ? ankle x 92

  20. The end of the galactic cosmic ray energy spectrum - a phenomenological view Extrapolation of direct measurements to high energies Flux compatible with air shower observations Cut-off for elemental energy spectra ~Z Spectra of heavy nuclei flatter due to fragmentation Knee caused by proton cut-off Second knee caused by end of galactic component (Z=92)?

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