Propagation and acceleration of High Energy CRs Jungyeon Cho (CNU, Korea)

“Interaction of CRs with MHD Turbulence” Q1. Do we need to consider MHD turbulence for ultra high energy CRs? * UHECRs come from Extra-Galactic sources

Local universe (~GZK radius) 30Mpc http://dolio.lh.net/~apw

Local universe (a bit smaller than the GZK radius) 3Mpc http://dolio.lh.net/~apw

Possible sources: radio galaxys, AGNs, shocks,… (Jones’ and Ryu’s talks) cluster: shock surfaces From T. Jones

The Universe is magnetized! cluster Photons have zero charge fi travel in geodesics (straightest lines) point back to source Extra-galactic B -Clusters: 1-10 mG & lc ~ 10kpc? -Filaments:~0.1 mG -Voids: <~10-3 mG deflected by Magnetic Fields a few Mpc

Magnetic field can deflect charged particles! B dv ----- = (v x B) (e/gmc) dt v2/r = evB/gmc rL=E/eB

Turbulent B field (B0 ~ b) Figure by S. Das

Low energy particles stay longer in clusters a few Mpc Photons have zero charge fi travel in geodesics (straightest lines) point back to source High E ( E > 1019 eV) Low E deflected by Magnetic Fields B~1-10 mG & lc ~ 10kpc rL ~ 1 kpc (E/1018eV)(B/1mG)-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!

Outside clusters, magnetic fields are weaker Deflection of particle is smaller (Dolag’s talk) * Magnetic lensing can be still important source E>1018-19 eV Galaxy

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,…

Galactic B Our Galaxy -mol. clouds: > 10 mG -disk: 5-8 mG -halo: ~1 mG ? Our Galaxy

Galactic sources : supernova remnants, winds, … (Biermann’s talk)

rL ~ 1 kpc (E/1018eV)(B/1mG)-1 B in disk ~ a few mG B in halo < ~ 1 mG (lc < ~100pc) MHD turbulence is important for Galactic CRs with E < 1016-17 eV

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 wall Vptl Dp/p ~ +V/Vptl V Vptl Dp/p ~ -V/Vptl V After many collisions, Dp/p ~ V/Vptl (No. of collisions)1/2

Example: acceleration by MHD turbulence VA Dv per back-scattering ~ vA (=Alfven speed) Dp/p ~ VA/Vptl

Dp ~ (Dp)2/Dt Dt Dp p t p shows a random walk-like behavior diffusion in momentum space Dp ~ ??? In spatial diffusion case: diffusion coefficient ~ Vptl lmfp ~ lmfp2/t

What makes p change? VA 1. Pitch-angle scattering: Dp/ p ~ (VA/Vptl), Dt ~ 1/n => Dp ~ p2(VA/Vptl)2n scattering freq. 2. Large scale compressible motions: Dp =? , Dt = ?

Large scale compressible motions Fact1: Compression in perpendicular direction increases momentum B Fact2: Compression in parallel direction increases momentum Conclusion: V matters! *Earlier studies in this direction: Ptuskin (1998); Chandran (2003)

Large scale compressible motions - (Dp/Dt) / p ~ V - Dt =? fast diffusion Dt ~ l||2/D|| slow diffusion Dt ~twave Dp~(Dp)2/Dt ~ p2(V )2 Dt ~ p2(V )2 twave We need to know V .

B 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 -Alfven and slow modes are elongated along B -Slow modes are passive (Slow modes follow Alfvenic time scales) -Fast modes are NOT elongated fast Lithwick & Goldreich (01); Cho & Lazarian (02; 03)

Acceleration by fast modes *Small scales contribute more Vl ~ Vl,fast / l When diffusion is slow, Dt ~ 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 In general, fast modes are more efficient than slow modes .

Acceleration by fast modes Dp Larger than 1 for slow diffusion case b=Pgas/PB slow diffusion

Acceleration by slow modes *All scales contribute equally When diffusion is slow:Dt ~ L||/VA Dp  p2(V )2 (L|| / VA ) ~ p2VL,slow2 / (L|| VA) ~ (p2VA/L) (VL,slow / VA) 2

Acceleration by slow modes: results Dp slow diffusion Note: QTD=1, if particles are tied to B =ln(LVA/D), if particles can move to different B lines See Chandran (2003)

Acceleration by pitch-angle scattering What is pitch-angle scattering? l E field

Acceleration by pitch-angle scattering VA Dv per back-scattering ~ vA (=Alfven speed) Dp / p ~ (VA/Vptl), Dt ~ 1/n scattering freq. Dp ~(Dp)2/Dt ~ p2(VA/Vptl)2n ~ p2(VA/Vptl)2 (Vptl/lmfp) ~ (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 lc Dq~ lc /rL r lc rL Random walk => (r/ lc)1/2 Dq ~(rlc )1/2/ rL

Effects of weak B field Deflection If Blc1/2 < 10-8 G Mpc1/2, small deflection, If Blc1/2 > 10-8 G Mpc1/2, diffusion, Time delay ( <=CRs arrive later than light) *Similar to the typical lifetime of AGNs ? Formulae from Lemoine (05)

Magnetic lensing initially uniformly distributed Figure by H.K. Kim initially uniformly distributed Initially particles are located in the yellow plane. We marked the position of the particles when they cross this plane B

Summary Dpfast ~ (p2VA/L)(LVA/lmpfVptl)a when diffusion is slow 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 anisotropy Dpfast ~ (p2VA/L)(LVA/lmpfVptl)a when diffusion is slow