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Propagation and acceleration of High Energy CRs
Jungyeon Cho (CNU, Korea)
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Q1. Do we need to consider MHD turbulence for ultra high energy CRs?
* UHECRs come from Extra-Galactic sources
“Interaction of CRs with MHD Turbulence”
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Local universe (~GZK radius)
http://dolio.lh.net/~apw
30Mpc
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3Mpc
Local universe (a bit smaller than the GZK radius)
http://dolio.lh.net/~apw
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Possible sources: radio galaxys, AGNs, shocks,…
cluster:shocksurfaces
From T. Jones
(Jones’ and Ryu’s talks)
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Photons have zero chargefi travel in geodesics(straightest lines)point back to source
deflected by Magnetic Fields
The Universe is magnetized!
Extra-galactic B
-Clusters: 1-10 G
& lc ~ 10kpc? -Filaments:~0.1 G-Voids: <~10-3 G
cluster
a few Mpc
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Magnetic field can deflect charged particles!
B
118
)1
)(10
(1
G
B
eV
E
Z
kpcrL
dv----- = (v x B) (e/mc) dt
v2/r = evB/mcrL=E/eB
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Turbulent B field (B0 ~ b)
Figure by S. Das
B0
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Photons have zero chargefi travel in geodesics(straightest lines)point back to source
deflected by Magnetic Fields
Low energy particles stay longer in clusters
B~1-10 G &
lc ~ 10kpc
cluster a few Mpc
High E ( E > 1019 eV)
Low E
rL ~ 1 kpc (E/1018eV)(B/1G)-1
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So, UHECRs with E > 1019 eV can escape the ICM without showing significant deflections =>Turbulence may not be very important for these particles * But, magnetic lensing can be still important.
CRs with E < 1019 eV spend a lot of time in clusters. => They interact with ICM turbulence => They can be accelerated by turbulence!
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Galaxysource E>1018-19 eV
Outside clusters, magnetic fields are weakerDeflection of particle is smaller (Dolag’s talk) * Magnetic lensing can be still important
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Q2. OK. MHD turbulence may be important in the ICM even for UHECRs. Then, is it also important in our Galaxy?
Yes. It’s also important for Galactic CRs, solar CRs,…
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Our Galaxy
Galactic B-mol. clouds: > 10 G-disk: 5-8 G
-halo: ~1 G ?
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Galactic sources : supernova remnants, winds, … (Biermann’s talk)
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MHD turbulence is important for Galactic CRs with E < 1016-17 eV
rL ~ 1 kpc (E/1018eV)(B/1G)-1
B in disk ~ a few G
B in halo < ~ 1 G
(lc < ~100pc)
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MHD turbulence and CRs
• MHD turbulence can accelerate and/or scatter CRs.
*Acceleration by MHD turbulence: - large-scale compressible motion - pitch-angle scattering
*Note: astrophysical acceleration mechanisms:
- Shock acceleration - Turbulence (2nd order Fermi acceleration) - Direct acceleration by electric field - …
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Q3. Then, how can MHD turbulence accelerate CRs?
assumption: rL < lc
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2nd order Fermi acceleration
V
Vptl
p/p ~ +V/Vptl
Vptl
wall
V
p/p ~ -V/Vptl
After many collisions, p/p ~ V/Vptl (No. of collisions)1/2
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Example: acceleration by MHD turbulence
v per back-scattering ~ vA (=Alfven speed)
p/p ~ VA/Vptl
VA
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t
p
p shows a random walk-like behaviordiffusion in momentum spaceDp ~ ???
In spatial diffusion case: diffusion coefficient ~ Vptl lmfp ~ lmfp
2/
Dp ~ (p)2/t
t
p
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What makes p change?
1. Pitch-angle scattering:
VA
p/ p ~ (VA/Vptl), t ~ 1/=> Dp ~ p2(VA/Vptl)2
scattering freq.2. Large scale compressible motions:
p =? , t = ?
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Large scale compressible motions
Fact1: Compression in perpendicular direction increases momentum
B
Conclusion: V matters! *Earlier studies in this direction: Ptuskin (1998); Chandran (2003)
Fact2: Compression in parallel direction increases momentum
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Large scale compressible motions
p/t) / p ~ V
t =?
fast diffusiont ~ l||2/D||
slow diffusiont ~twave
Dp~(p)2/t ~ p2(V )2 t ~ p2(V )2 twave
We need to know V .
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There are two compressible modes in magnetized fluids:
slow and fast modes
* Alfven modes are not compressible
B
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Slow & fast waves
Cho, Lazarian, & Vishniac (2003)
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Structure of MHD turbulence
-Alfven and slow modes are elongated along B
-Slow modes are passive (Slow modes follow
Alfvenic time scales)
Lithwick & Goldreich (01); Cho & Lazarian (02; 03)
Alfven
-Fast modes are NOT elongated
fast
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Acceleration by fast modes
When diffusion is slow, t ~ l/Cf (wave period)
Dp p2(Vl )2 (l/Cf)
~ p2Vl,fast2 /(l Cf)
~ (p2VA / l)(Vl,fast /Cf)2(Cf/VA)* Cf=speed of fast wave
Vl ~ Vl,fast / l
*Small scales contribute more
In general, fast modes are more efficient than slow modes.
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Acceleration by fast modes
Dp
slow diffusionLarger than 1 for slow diffusion case
=Pgas/PB
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Acceleration by slow modes
When diffusion is slow:t ~ L||/VA
Dp p2(V )2 (L|| / VA )
~ p2VL,slow2 / (L||
VA)
~ (p2VA/L) (VL,slow / VA) 2
*All scales contribute equally
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Acceleration by slow modes: results
Dp
Note: QTD=1, if particles are tied to B =ln(LVA/D), if particles can move to different B lines
See Chandran (2003)
slow diffusion
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What is pitch-angle scattering?
Acceleration by pitch-angle scattering
E field
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Acceleration by pitch-angle scattering
v per back-scattering ~ vA (=Alfven speed)
p / p ~ (VA/Vptl), t ~ 1/ scattering freq.
VA
~ p2(VA/Vptl)2 (Vptl/lmfp)
Dp ~(p)2/t ~ p2(VA/Vptl)2
~ (p2VA/L)(LVA/Vptllmfp) ~(p2VA/L)(tL,diff/ tL,wave)
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Acceleration by pitch-angle scattering
More efficient than slow or fast modes when diffusion is slow
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4.What happens when B is weak?
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Deflection of CRs by weak B
B
~ lc /rL
rL
lc
Random walk => (r/ lc)1/2 ~(rlc )1/2/ rL
r
lc
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Effects of weak B field
-Deflection
-Time delay ( <=CRs arrive later than light)
•If Blc1/2 < 10-8 G Mpc1/2, small deflection,
•If Blc1/2 > 10-8 G Mpc1/2, diffusion,
*Similar to the typical lifetime of AGNs ?
Formulae from Lemoine (05)
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Magnetic lensing
B
Initially particles are located in the yellow plane.
We marked the position of the particles when they cross this planeFigure by H.K. Kim
initially uniformly distributed
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Summary•MHD turbulence can accelerate charged particles•Fast modes are more efficient than slow modes•Pitch-angle scattering is more efficient than fast or slow modes when diffusion is slow•Magnetic lensing may be important for small scale anisotropyDp
fast ~ (p2VA/L)(LVA/lmpfVptl)when diffusion is slow