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