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

Jörg R. HörandelUniversity of Karlsruhe

Workshop on the Physics of the End of the Galactic Cosmic Ray SpectrumAspen, April 25th – 30th, 2005

knee 2nd knee

Nag

ano

& W

atso

n, R

ev. M

od. P

hys.

72

(200

0) 6

89direct indirect

x 92

Results from direct measurements (Z=1-28)

protons

ironExtrapolate power law spectra

to high energies

JRH, Astropart. Phys 19 (2003) 193

EscapeLeakage from Galaxy

Shape of energy spectrum

fragmentation ~ A2/3

EscapeLeakage from Galaxy

The poly-gonato model• 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

A

EAZ

mME

eME

ME

mEENE

dE

d Z

2

)780()2()(

410*5.2

at low energies: solar modulation

above knee: common c

c

Zc

c

Z

ε

γγε

Z

0γ0

0Z0

0

Z

E

E1EΦ)(E

dE

dΦ

above knee: common

cc

Z

ε

Δγε

Z

0γ0

0Z0

0

Z

E

E1EΦ)(E

dE

dΦ

above Z*10 GeV: power laws with cut-off

p

p

p

Z

E

AE

ZE

Ecut-off energy

rigidity dependent

mass dependent

constant

link direct and indirect measurements

JRH, Astropart. Phys 19 (2003) 193

abundance at ~1 GeV/n spectral index vs nuclear charge

CZ ZBAγ

Elements heavier than iron (Z=29-92)

JRH, Astropart. Phys 19 (2003) 193

A = 2.70 +/- 0.19B = (-8.34 +/- 4.67) 10-4

C = 1.51 +/- 0.13

Cosmic-ray energy spectrum

renormalizeenergyscale

JRH, Astropart. Phys 19 (2003) 193

Fit to the all-particle spectrum with rigidity dependent cut-off

common c

0.1162/dof

1.87 +- 0.18c

-4.68 +- 0.23c

4.51 +- 0.52Ep [PeV]

c

Zc

c

Z

ε

γγε

p

0γ0

0Z0

0

Z

EZ

E1EΦ)(E

dE

dΦ

0.1132/dof

1.90 +- 0.19c

2.10 +- 0.24

4.49 +- 0.51Ep [PeV]

common

cc

Z

ε

Δγε

p

0γ0

0Z0

0

Z

EZ

E1EΦ)(E

dE

dΦ

Fit result compared to indirect measurements

Diffusion Model

z)Q(r,z)N(r,z

)(rDrr

1

r)(D

zzD

zrrD

rr

1AA

transport equation

0.30.2m;Z

ED

m

Z

EDA

transverse diffusion coefficient

hall diffusion coefficient

particleconcentration

source term

kpc)4δ(r~Q(r)

large halo modelwith antisymmetric regular magnetic fieldV.S. Ptuskin et al., A&A 268 (1993) 726

Propagation of cosmic rays through Galaxy

Diffusion modelV.S. Ptuskin et al., A&A 268 (1993) 726N.N. Kalmykov, A.I. Pavlov, 26th ICRC 4 (1999) 263

JRH, Kalmykov, Timokhin

proton

Propagation path length in Galaxy

JRH, Kalmykov, Timokhin

diffusion model

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

Ratio of secondary to primary nucleiACE/CRIS

Leaky box model

1.40.58

2

escGV1.4βR/GV1.0βR/

βg/cm26.7λ

20.6

g/cm0.013GV10

R*6.0λ

Propagation pathlength in Galaxy

S.P. Swordy, 24th ICRC, Rome 2 (1995) 697

residual pathlength model

diffusion model

1.40.58

2

GV1.4βR/GV1.0βR/

βg/cm26.7λ

leaky box model

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

8 kpc * 1 p/cm3

~E-0.2

Anisotropy amplitude vs energy

T. Antoni et al, ApJ 604 (2004) 687

2

1

2

1

cos2

sin2

n

ii

n

ii nn

R

Rayleigh vector

V.S. Ptuskin, Adv. Space Res. 19 (1997) 697J. Candia et al., J. Cosmol. Astropart. Phys. 5 (2003) 3

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

Age of cosmic raysACE/CRIS

15*106 a

diffusion model

~E-0.05

JRH, Kalmykov, Timokhin

fragmentation ~ A2/3

EscapeLeakage from Galaxy

Shape of energy spectrum

Fraction of surviving nuclei during propagation

JRH, Kalmykov, Timokhin

Matter traversed by protonsheavy nuclei E~Z Fraction of surviving nuclei

QGSJET

+cross sections from QGSJET

>~50% of nuclei survivewithout interaction

Cosmic-ray energy spectrum

?

according to Astropart. Phys. 19 (2003) 193

knee 2nd kneeankle

?

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

Knee caused by proton cut-off

Second knee caused by end of galactic component (Z=92)?

Spectra of heavy nuclei flatter due to fragmentation

Cut-off for elemental energy spectra ~Z