Midwest Magnetic Field 2011

MotivationTheoryResults

Discussion

Acceleration of Cosmic-rays by Super-Alfvenic turbulence

Hyeseung LeeUniversity of Wisconsin-Madison

Alex LazarianUniversity of Wisconsin-Madison

Reinhard SchlikeiserUniversity of Bochum, Germany

Cosmic RayGalaxy Cluster

Cosmic Ray Spectrum

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1GeV ~ Knee : Galactic Origin (Supernovae)

Knee ~ Ankle: Larger Shocks (Galactic wind - Neutron Stars, Superbubbles, Reaccelerated heavy

nuclei) and SN explosions into stellar windsUHECR (Ultra High Energy Cosmic rays)

Slope ϒ=-2.7

Slope ϒ=-3.1

Slope ϒ=-2.7

MotivationTheoryResults

Discussion

Viktor Hess(1912)

Galaxy Cluster

Hillas Plot

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UHECR (Ultra High Energy Cosmic rays)

Extragalactic (GRB, AGN, Galaxy Cluster)

MotivationTheoryResults

Discussion

rlar < L

It need astrophysical acceleration mechanism

Stochastic Acceleration

Second-order Fermi Acceleration

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Fermi(1949)Galactic CRs are acceleratedas the result of many collision with massive, magnetized cloud

Particle in head-on collisions gains energyParticle in an overtaking collisions loses energy

θexit : <cosθout’> = 0θenter : ν - Vcosθin

On average,net energy gain

MotivationTheoryResults

Discussion

But, head-on collisions are more frequentStochastic Acceleration by MHD turbulence

Acceleration by MHD turbulenceMotivation

TheoryResults

Discussion

Property of MHD Turbulence

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The acceleration by sub-Alfvenic turbulence had been discussed by Cho & Lazarian 2006.

Sub-Alfvenic turbulence ( Vl < VA )(Cho & Lazarian 2006)

Super-Alfvenic turbulence ( Vl > VA )

35A kkE 35s kkE

23f kkE

Goldreich-Sridhar 95 scaling

ISOTROPIC

Super-Alfvenic turbulence evolves along the hydrodynamic isotropic Kolmogorov cascade

Assume that compression follows Kolmogorov scaling

For example :

Cho & Larzarin (2002)

MHD turbulenceMotivation

TheoryResults

Discussion

Diffuse by MHD turbulence

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MHD turbulence can change particle momentum Diffusion Coefficient

MHD turbulenceMotivation

TheoryResults

Discussion

Diffuse by MHD turbulence

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MHD turbulence can change particle momentum Diffusion Coefficient

Pitch-angle Scattering

MHD turbulenceMotivation

TheoryResults

Discussion

Diffuse by MHD turbulence

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MHD turbulence can change particle momentum Diffusion Coefficient

Pitch-angle Scattering

Large-scale compressible motion

Fast diffusion time

Slow diffusion time

MHD turbulenceMotivation

TheoryResults

Discussion

Diffuse by MHD turbulence

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MHD turbulence can change particle momentum Diffusion Coefficient

Pitch-angle Scattering

Large-scale compressible motion

Fast diffusion time

Slow diffusion time

The acceleration by large-scale turbulence is relative to the momentum diffusion coefficient

MHD turbulenceMotivation

TheoryResults

Discussion

Comparison of D

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tvptp

222

pDPitch-angle Scattering

Large scale compression Fast Diffusion Limits Slow Diffusion Limits

ptlmfp

AA

vlLv

Lvp2~pitch

pD

DL

LvL

2

~ t , vA

A

A vv

t , v~

ptlmfp

A

A

LA

vlLv

vv

Lvp

22

~Alf-suppD A

A

LA Mvv

Lvp

22

~

Alf-suppD

For super-alfvenic turbulence, pitchalfvensuppp DD

Large-Scale motion dominates acceleration of cosmic- ray !!!

SUMMARY1. Super-Alfvenic turbulence is present in astrophysicsal environment

: galaxy clusters

2. For super-Alfvenic acceleration by large scale motions dominates resonance scattering.

3. The acceleration by super-Alfvenic turbulence should be taken into account in models for galaxy cluster and molecular cloud.

MotivationTheoryResults

Summary

Midwest Magnetic Field 2011