Propagation and acceleration of High Energy CRs
Jungyeon Cho (CNU, Korea)
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”
Local universe (~GZK radius)
http://dolio.lh.net/~apw
30Mpc
3Mpc
Local universe (a bit smaller than the GZK radius)
http://dolio.lh.net/~apw
Possible sources: radio galaxys, AGNs, shocks,…
cluster:shocksurfaces
From T. Jones
(Jones’ and Ryu’s talks)
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
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
Turbulent B field (B0 ~ b)
Figure by S. Das
B0
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
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!
Galaxysource E>1018-19 eV
Outside clusters, magnetic fields are weakerDeflection of particle is smaller (Dolag’s talk) * Magnetic lensing can be still important
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,…
Our Galaxy
Galactic B-mol. clouds: > 10 G-disk: 5-8 G
-halo: ~1 G ?
Galactic sources : supernova remnants, winds, … (Biermann’s talk)
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)
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 - …
Q3. Then, how can MHD turbulence accelerate CRs?
assumption: rL < lc
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
Example: acceleration by MHD turbulence
v per back-scattering ~ vA (=Alfven speed)
p/p ~ VA/Vptl
VA
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
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 = ?
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
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 .
There are two compressible modes in magnetized fluids:
slow and fast modes
* Alfven modes are not compressible
B
Slow & fast waves
Cho, Lazarian, & Vishniac (2003)
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
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.
Acceleration by fast modes
Dp
slow diffusionLarger than 1 for slow diffusion case
=Pgas/PB
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
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
What is pitch-angle scattering?
Acceleration by pitch-angle scattering
E field
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)
Acceleration by pitch-angle scattering
More efficient than slow or fast modes when diffusion is slow
4.What happens when B is weak?
Deflection of CRs by weak B
B
~ lc /rL
rL
lc
Random walk => (r/ lc)1/2 ~(rlc )1/2/ rL
r
lc
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)
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
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