1. Cosmic Ray (CR) transport in MHD turbulence Huirong Yan Kavli Institute of Astronomy & Astrophysics, Peking U

2. Outline Discovery of CRs and importance of the studies of transport processes. Basic formalism and interaction mechnism. Cosmic Ray (CR) scattering by numerically tested models of turbulence. Turbulence generation and particle confinement at shocks Instabilities and Back-reaction of CRs (small scale) Implications for various astrophysical problems Insight into Gamma Ray Burst

3. What are Cosmic rays? Cosmic rays: energetic charged particles from space.

4. Observational distribution of CRS Icecube measurement M. Duldig 2006 Highly isotropic

5. Importance of CR propagation CMB synchrotron foreground Diffuse ɣ ray emission diffuse Galactic 511 keV radiation Identification of dark matter

6. Importance of CR acceleration: Fermi II Stochastic Acceleration: Fermi (49) Gamma ray burst Solar Flare

7. Importance to Fermi I acceleration Pre-shock Post-shock region region Shock front Shock Acceleration Turbulence generated by shock Turbulence generated by streaming Tycho’s remanent Krymsky 77, Axford et al 77, Bell 78, Blandford & Ostriker 78, Drury 83 Diffusion of CRs

8. More data are available for model fitting

9. Big simulation itself is not adequate big numerical simulations fit results due to the existence of "knobs" of free parameters (see, e.g., http://galprop.stanford.e du/). http://galprop.stanford.e du Self-consistent picture can be only achieved on the basis of theory with solid theoretical foundations and numerically tested.

10. Basic equations In case of small angle scattering, Fokker-Planck equation can be used to describe the particles’ evolution: Cosmic Rays Magnetized medium S : Sources and sinks of particles 2nd term on rhs: diffusion in phase space specified by Fokker -Planck coefficients D xy

11. Fokker Planck (FP)diffusion coeffcients

12. FP coefficients can be used to find transport and accleration properties ~ ~ ~ Propagation Stochastic Acceleration D   B, D pp  Ε    Where do  B,  come from? MHD turbulence! The diffusion coeffecients are primarily determined by the statistical properties of turbulence

13. Resonance mechanism Gyroresonance  - k || v || = n  (n = ± 1, ± 2 …), Which states that the MHD wave frequency (Doppler shifted) is a multiple of gyrofrequency of particles (v || is particle speed parallel to B). So, k ||,res ~ /v = 1/r L B rLrL large scale perturbation, adiabatic invariant small scale averaged out large scale perturbation, adiabatic invariant small scale averaged out

14. Transit Time Damping (TTD) Transit time damping (TTD) Compressibility of B field required! no resonant scale All scales contribute Scattering due to TTD Landau resonance condition:  k || v || v A =  k v || cos   v A / vcos  mirror effect is a result of adiabatic invariant! small amplitude needs comoving mirror effect is a result of adiabatic invariant! small amplitude needs comoving

15. Betatron Acceleration by Compressible Turbulence Traditionally, Betatron acceleration was only considered behind shocks. Turbulence, however, can also compress the magnetic field and therefore accelerate dust through the induced electric field ( Berger et al 1958; Kulrud & Pearce 1971; Cho & Lazarian 2006; Yan 2009 ). particle orbit

16. Turbulence is ubiquitous! Extended Big Power Law Armstrong et al. (1995), Chepurnov & Lazarian (2009) Supernovae blow interstellar "bubbles" turbulent LMC Re VL/  10 10 >> 1  r L v th, v th < V, r L << L

17. Models of MHD turbulence Ad hoc turbulence models Tested models of MHD turbulence 1. Alfven and slow modes: Goldreich-Sridhar 95 scaling 2. Fast modes: isotropic, similar to accoustic turbulence Slab model: Only MHD modes propagating along the magnetic field are counted. Kolmogorov turbulence: isotropic, with 1D spectrum E(k)~k -5/3

18. Alfven and slow modes (GS95) fast modes B Numerically tested models for MHD turbulence Alfven slow fast ~k -5/3 ~k -3/2 Equal velocity correlation contour ( Cho & Lazarian 02, Kowal & Lazarian 2010 ) anisotropic eddies

19. scattering efficiency is reduced l  << l || ~ r L 2. “steep spectrum” E(k  )~ k  -5/3, k  ~ L 1/3 k || 3/2 E(k || ) ~ k || -2 steeper than Kolmogorov! Less energy on resonant scale eddies B l || ll 1. “ random walk” B Contrary to common belief: Scattering in Alfvenic turbulence is negligible! 2r L

20. The often adopted Alfven modes are useless. Alternative solution is needed for CR scattering (Yan & Lazarian 02,04)? Scattering frequency (Kolmogorov) Alfven modes Big difference!!! Alvenic turbuelence cannot scatter cosmic rays! Kinetic energy ? Remarkable isotropy δ~6x10 - 4 and long age 10 7 yrs ? Remarkable isotropy δ~6x10 - 4 and long age 10 7 yrs (Chandran 2000) Total path length is ~ 10 4 crossings at GeV from the primary to secondary ratio.

21. fast modes are dominant! modesmode s momodes Depends ondamping dam damping Fast modes are identified as the dominate source for CR scattering ( Yan & Lazarian 2002, 2004 )! fast modes plot w. linear scale Scattering frequency Kinetic energy

22. Linear damping of fast waves Viscous damping ( Braginskii 1965 ) Collisionless damping ( Ginzburg 1961, Foote & Kulsrud 1979 ) Increase with plasma  P gas /P mag and the angle  between k and B.

23. damping in turbulent medium  complication: finite randomization of  during cascade Randomization of local B: field line wandering by shearing via Alfven modes: dB/B ≈ (V/L) 1/2 t k 1/2 Randomization of wave vector k: dk/k ≈ (kL) -1/4 V/V ph B k  Lazarian, Vishniac & Cho 2004 Field line wandering Field line wandering is necessary to account for!

24. Observed secondary elements supports scattering by fast modes! Scattering by fast modes

25. kcLkcL 1au 1pc With randomization Anisotropy of fast modes arising from damping Cutoff scale in different media Wave pitch angle ISM phases Wave pitch angle Damping depends on medium. Anisotropic damping results in quasi-slab geometry. Field line wandering should be accounted for. halo WIM Yan & Lazarian (2008) With randomization Solar corona Petrosian, Yan, & Lazarian (2006)

26. Application to stellar wind heating by collisionless damping is dominant in rotating stars ( Suzuki, Yan, Lazarian, & Casseneli 2005 ). B

27. Comparison w. test particle simulation a realistic fluctuatating B fields from numerical simulations – Particle trajectory — Magnetic field

28. Results of Monte-Carlo simulations Particle scattering in incompressible turbulence D  / ~r (TTD) D  / ~r 2.5 (gyroresonance) — gyration frequency, L — outer scale of turbulence. (obtained from quality-controlled particle tracer, Beresnyak, Yan & Lazarian 2010 ) μ=0.5

29. CR Transport varies from place to place! Flat dependence of mean free path can occur due to collisionless damping. CR Transport in ISM Mean free path (pc) Kinetic energy halo WIM Text from Bieber et al 1994 Palmer consensus

30. Detailed study of solar flare acceleration must include damping, nonlinear effects TTD Acceleration by fast modes is an important mechanism to generate energetic electrons in Solar flares ( Yan, Lazarian & Petrosian 2008 ). Comparison of rates Kinetic energy Loss Escape Acceleration With randomization Solar corona Petrosian, Yan, & Lazarian (2006) Loss Wave pitch angle

31. Idea of fast modes takes over in other fields Brunetti & Lazarian (2007)

32. Dust dynamics is dominated by MHD turbulence! Grains can reach supersonic speed due to acceleration by turbulence and this results in more efficient shattering and adsorption of heavy elements ( Yan & Lazarian 2003, Yan 2009 ). velocity of charged grains Grain size 1km/s!

33. What are the implications for dust dynamics? Extinction curve varies according to local Conditions of turbulence ( Hirachita & Yan 2009 ). Extinction curve Evolving grain size distribution in turbulence 50 Myr 100 Myr 50 Myr 100 Myr initial

34. Interaction w. small scale waves: Streaming instability Acceleration in shocks requires scattering of particles back from the upstream region. Downstream Upstream Turbulence generated by shock Turbulence generated by streaming Streaming cosmic rays result in formation of perturbation that scatters cosmic rays back and increases perturbation. This is streaming instability that can return cosmic rays back to shock and may prevent their fast leak out of the Galaxy.

35. Streaming instability is suppressed in background turbulence! In turbulent medium, wave-turbulence interaction damps waves ( Yan & Lazarian 2002, 2004, Farmer & Goldreich 2004, Beresnyak & Lazarian 2008 ). B

36. Streaming instability of CRs is suppressed (Cont.) 2. Calculations for weak case (  B<B): With background compressible turbulence ( Yan & Lazarian 2004 ): Ε max ≈ 1.5 10 -9 [n p -1 (V A /V) 0.5 (Lc  /V 2 ) 0.5 ] 1/1.1 E 0 This gives Ε max ≈ 20GeV for HIM. Similar estimate was obtained with background Alfvenic turbulence ( Farmer & Goldreich 2004 ). 1.MHD turbulence can suppress streaming instability ( Yan & Lazarian 2002 ).

37. Alternative for upstream tubulence? Beresnyak, Jones & Lazaian (2009)

38. Implication: Magnetically limited X-ray filaments in young SNRs Strong magnetic field produced by streaming instability at upstream of the shock, may be damped by turbulence at downstream, generating filaments of a thickness of 10 16 - 10 17 cm ( Pohl, Yan & Lazarian 2005 ). Chandra

39. Feedback of CRs on MHD turbulence Slab modes with Lazarian & Beresnyak 2006, Yan & Lazarian 2011

40. Wave Growth is limited by Nonlinear Suppression! Turbulence compression Scattering by instability generated slab wave A β ≝ Pgas/P mag < 1, fast modes ( isotropic cascade +anisotropic damping ) β > 1 slow modes ( GS95 )

41. Scattering by growing waves Anisotropy cannot reach δv/v A, the predicted value earlier, and the actual growth is slower and smaller amplitude due to nonlinear suppression ( Yan &Lazarian 2011 ). By balancing it with the rate of increase due to turbulence compression, we can get Bottle-neck of growth due to energy constraint: Simple estimates:

42. domains for different regimes of CR scattering Damped by background turbulence λ fb cutoff due to linear damping

43. SummarySummary Changes in the MHD turbulence paradigm necessitates revision of CR theories. Compressible fast modes dominates CR transport through direct scattering. CR transport therefore varies from place to place. Slab waves are naturally generated in compressible turbulence by the gyroresonance instability, which dominates the scattering of low energy CRs (<100GeV). Instabilities are subjected to damping by background turbulence. Implications are wide from solar flares to cluster of galaxies. For perpendicular transport: Perpendicular transport

44. Future perspective etc… Fermi Acceleration in solar flares, GRBS, and radio halos Acceleration in solar flares, GRBS, and radio halos modeling CR transport in clusters GRBS, and radio halos modeling CR transport in clusters GRBS, and radio halos revisit shock acceleration Applicability GRBS, and radio halos Applicability diffuse gamma ray emission synchrotron foreground emission CR transport in Galaxy due to compressible modes Full numerical testing in incompressible and compressible medium GRBS, and radio halos Full numerical testing in incompressible and compressible medium GRBS, and radio halos Clarification of modeling knee and streaming instability

45. Quasilinear theory is not adequate Long standing problem: 90 degree scattering K res = /v || →∞, the scale is below the dissipation scale of turbulence No scattering at 90 o ?  || →∞?! A key assumption in Quasilinear theory: guiding center is unperturbed Z 0 =v  t  Nonlinear theory: In reality, the guiding center is perturbed, especially on large scales, z=(v   Δv || ) t.

46. Nonlinear broadening of resonance solves the 90 o problem! On large scale, unperturbed orbit assumption in QLT fails due to conservation of adiabatic invariant v  2 /B (Volk 75). Pitch angle cosine Broadened resonance varying v ⊥ varying v || -∆ vtvt v || t ∆ Test particle simulation Scattering due to transit time damping (TTD, cf. Schlickeiser & Miller 1998 ) QLT NLT Yan & Lazarian (2008)