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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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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


Results from direct measurements (Z=1-28)

protons

Extrapolate power law spectra

to high energies

iron

JRH, Astropart. Phys 19 (2003) 193


Shape of energy spectrum

Escape

Leakage from Galaxy

Escape

Leakage from Galaxy

fragmentation

s ~ A2/3


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


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


Cosmic-ray energy spectrum

renormalizeenergy

scale

JRH, Astropart. Phys 19 (2003) 193


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


Fit result compared to indirect measurements


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


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


Propagation pathlength in Galaxy

diffusion model

JRH, Kalmykov, Timokhin


Ratio of secondary to primary nuclei

ACE/CRIS

Leaky box model

N. E. Yanasak, ApJ 563 (2001) 768


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


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


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


Shape of energy spectrum

fragmentation

s ~ A2/3

Escape

Leakage from Galaxy


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


Cosmic-ray energy spectrum

?

according to Astropart. Phys. 19 (2003) 193


knee

2nd knee

?

ankle

x 92


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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