Propagation and acceleration of High Energy CRs

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

2. “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

3. 30Mpc Local universe (~GZK radius) http://dolio.lh.net/~apw

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

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

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

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

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

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

10. 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!

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

12. 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,…

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

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

15. 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

16. 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 - …

17. assumption: rL < lc Q3. Then, how can MHD turbulence accelerate CRs?

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

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

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

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

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

23. 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 . Large scale compressible motions - (Dp/Dt) / p ~ V - Dt =?

24. B There are two compressible modes in magnetized fluids: slow and fast modes * Alfven modes are not compressible

25. Slow & fast waves Cho, Lazarian, & Vishniac (2003)

26. Alfven -Fast modes are NOT elongated fast 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)

27. 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 *Small scales contribute more Vl ~ Vl,fast / l

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

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

30. 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 slow modes: results Dp slow diffusion

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

32. VA Dp / p ~ (VA/Vptl), Dt ~ 1/n scattering freq. Acceleration by pitch-angle scattering Dv per back-scattering ~ vA (=Alfven speed) • Dp~(Dp)2/Dt ~ p2(VA/Vptl)2n ~ p2(VA/Vptl)2 (Vptl/lmfp) ~ (p2VA/L)(LVA/Vptllmfp) ~(p2VA/L)(tL,diff/ tL,wave)

33. Acceleration by pitch-angle scattering More efficient than slow or fast modes when diffusion is slow

34. 4.What happens when B is weak?

35. r lc Deflection of CRs by weak B B lc Dq~ lc /rL rL Random walk => (r/ lc)1/2 Dq ~(rlc )1/2/ rL

36. 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)

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

38. 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 • anisotropy Dpfast ~ (p2VA/L)(LVA/lmpfVptl)awhen diffusion is slow