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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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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

Aspen, April 25th – 30th, 2005


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

Results from direct measurements (Z=1-28)

protons

Extrapolate power law spectra

to high energies

iron

JRH, Astropart. Phys 19 (2003) 193


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

Shape of energy spectrum

Escape

Leakage from Galaxy

Escape

Leakage from Galaxy

fragmentation

s ~ A2/3


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

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


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

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


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

Cosmic-ray energy spectrum

renormalizeenergy

scale

JRH, Astropart. Phys 19 (2003) 193


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

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


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

Fit result compared to indirect measurements


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

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


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

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


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

Propagation pathlength in Galaxy

diffusion model

JRH, Kalmykov, Timokhin


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

Ratio of secondary to primary nuclei

ACE/CRIS

Leaky box model

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


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

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


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

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


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

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


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

Shape of energy spectrum

fragmentation

s ~ A2/3

Escape

Leakage from Galaxy


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

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


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

Cosmic-ray energy spectrum

?

according to Astropart. Phys. 19 (2003) 193


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

knee

2nd knee

?

ankle

x 92


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

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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