1. Interstellar Turbulence: Theory, Implications and Consequences Alex Lazarian ( Astronomy, Physics and CMSO ) Collaboration : H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov, E. Vishniac, G. Eyink, P. Desiati, G. Brunetti …

2. Theme 2. Propagation and Acceleration of Cosmic Rays in Turbulent Magnetic Fields

3. Icecube measurement 2010 M. Duldig 2006 Highly isotropic MHD turbulence theory induces changes on our understanding of CRs propagation and stochastic acceleration

4. Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence Perpendicular diffusion of cosmic rays Acceleation of cosmic rays by shocks in turbulent media Points of Part 2:

5. Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence Perpendicular diffusion of cosmic rays Acceleation of cosmic rays by shocks in turbulent media Points of Part 2:

6. 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 Cosmic rays interact with magnetic turbulence

7. Correct diffusion coefficients are the key to the success of such an approach

8. Turbulence induces second order Fermi process Magnetic “clouds”

9. Resonance and Transit Time Damping (TTD) are examples of 2nd order Fermi process B rLrL n=1 n=0

10. Diffusion in the fluctuating EM fields CollisionlessFokker-Planck equation Boltzmann-Vlasov eq  B,  v<<B 0, V (at the scale of resonance) Fokker-Planck coefficients : D  ≈  2 /  t, D pp ≈  p 2 /  t are the fundermental parameters we need. Those are determined by properties of turbulence!, For TTD and gyroresonance,  sc /  ac   sc /  ac  ≈ D pp / p 2 D  ≈ (V A /v) 2 Turbulence properties determine the diffusion and acceleration

11. ~ ~ ~ Propagation Stochastic Acceleration The diffusion coeffecients are determined by the statistical properties of turbulence The diffusion coefficients define characteristics of particle propagation and acceleration

12. Gyroresonance  (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, B rLrL Gyroresonance scattering depends on the properties of turbulence

13. scattering efficiency is reduced l  perp << l || ~ r L 2. “steep spectrum” steeper than Kolmogorov! Less energy on resonant scale eddies B l || ll 1. “ random walk” B 2r L Alfenic turbulence injected at large scales is inefficient for cosmic ray scattering/acceleration

14. Alternative solution is needed for CR scattering (Yan & Lazarian 02,04 Brunetti & Lazarian 0,). Scattering frequency (Kolmogorov) Alfven modes Big difference!!! Kinetic energy ( Chandran 2000) Total path length is ~ 10 4 crossings at GeV from the primary to secondary ratio. Inefficiency of cosmic ray scattering by Alfvenic turbulence is obvious and contradicts to what we know about cosmic rays

15. modesmode s momodes Depends on 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 Fast modes efficiently scatter cosmic rays solving problems mentioned earlier

16. Viscous damping ( Braginskii 1965 ) Collisionless damping ( Ginzburg 1961, Foote & Kulsrud 1979 ) Damping increases with plasma  P gas /P mag and the angle  between k and B. Damping is for fast modes is usually defined for laminar fluids and is not applicable to turbulent environments

17.  direction changes 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 To calculate fast mode damping one should take into account wandering of magnetic field lines induced by Alfvenic turbulence Magnetic field wandering induced by Alfvenic turbulence was described in Lazarian & Vishniac 1999 Yan & Lazarian 2004

18. 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 Modeling that accounts for damping of fast modes agrees with observations

19. Alfvenic turbulence is inefficient for scattering if it is generated on large scales. Fast modes dominate scattering, but damping of them is necessary to account for. Calculation of fast mode damping requires accounting for field wandering by Alfvenic turbulence. Scattering depends on the environment and plasma beta. Actual turbulence and acceleration in collisionless environments may be more complex Take home message 8:

20. Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence Perpendicular diffusion of cosmic rays Acceleation of cosmic rays by shocks in turbulent media Points of Part 2:

21. Perpendicular transport is due to turbulent B field Dominated by field line wandering. B0B0B0B0 – Particle trajectory — Magnetic field Intensive studies: e.g., Jokipii & Parker 1969, Forman 74, Urch 77, Bieber & Matthaeus 97, Giacolone & Jokipii 99, Matthaeus et al 03, Shalchi et al. 04 What if we use the tested model of turbulence?

22. Perpendicular transport M A < 1, CRs free stream over distance L, thus D ⊥ =R 2 /∆t= Lv || M A 4 Whether and to what degree CRs diffusion is suppressed depends on Alfven Mach number, i.e M A = V inj /V A. Lazarian & Vishniac 1999, Lazarian 2006, Yan & Lazarian 2008 Earlier works suggested M A 2 dependence

23. Predicted M A 4 suppression is observed in simulations! Differs from M 2 dependence in classical works, e.g. in Jokipii & Parker 69, Matthaeus et al 03. Xu & Yan 2013

24. Is Subdiffusion (∆x ~ ∝ t a, a<1) typical? Subdiffusion (or compound diffusion, Getmantsev 62, Lingenfelter et al 71, Fisk et al. 73, Webb et al 06) was observed in near-slab turbulence, which can occur on small scales due to instability. What about large scale turbulence? Example: diffusion of a dye on a rope a) A rope allowing retracing, ∆t =l rope 2 /D b) A rope limiting retracing within pieces l rope /n, ∆t =l rope 2 /nD Diffusion is slow if particles retrace their trajectories.

25. Is there subdiffusion (∆x 2 ∝ ∆t a, a<1) ? Subdiffusion (or compound diffusion, Getmantsev 62, Lingenfelter et al 71, Fisk et al. 73, Webb et al 06 ) was observed in near-slab turbulence, which can occur on small scales due to instability. Diffusion is slow only if particles retrace their trajectories.

26. In turbulence, CRs’ trajactory become independent when field lines are seperated by the smallest eddy size, l ⊥,min. The separation between field lines grows exponentially, provides L RR =| ||,min log(l ⊥,min /r L ) Subdiffusion only occurs below L RR. Beyond L RR, normal diffusion applies. l ,min – Particle trajectory — Magnetic field Subdiffusion does not happen in realistic astrophysical turbulence Lazarian 06, Yan & Lazarian 08

27. General Normal Diffusion is observed in simulations! Cross field transport in 3D turbulence is in general a normal diffusion! incompressible turbulence Beresnyak et al. (2011) compressible turbulence (Xu & Yan 2013 ) ∝ t r L /L 0.001 0.01 r L /L 0.001 0.01

28. Perpendicular propagation is superdiffusive on scales less than the injection scale Lazarian, Vishniac & Cho 2004 Magnetic field separation follows the law y 2_ x 3 (Richarson law), x<L inj x Xu & Yan 2013

29. Alfvenic Perpendicular diffusion scales as M A 4, not M A 2 Subdiffusion does not happen Superdiffusion takes place on scales smaller than the injection scale Take home message 9:

30. Scattering and second order Fermi acceleration of cosmic rays by MHD turbulence Perpendicular diffusion of cosmic rays Acceleation of cosmic rays by shocks in turbulent media Points of Part 2:

31. Acceleration in shocks requires scattering of particles back from the upstream region. Downstream Upstream Magnetic turbulence generated by shock Magnetic fluctuations generated by streaming Point 5. Turbulence alters processes of Cosmic Ray acceleration in shocks

32. Chandra In postshock region damping of magnetic turbulence explains X-ray observations of young SNRs Alfvenic turbulence decays in one eddy turnover time ( Cho & Lazarian 02 ), which results in magnetic structures behind the shock being transient and generating filaments of a thickness of 10 16 -10 17 cm ( Pohl, Yan & Lazarian 05 ).

33. B vAvA shock Streaming instability in the preshock region is a textbook solution for returning the particles to shock region

34. shock 1.Streaming instability is suppressed in the presence of external turbulence (Yan & Lazarian 02, Farmer & Goldreich 04, Beresnyak & Lazarian 08). 2.Non-linear stage of streaming instability is inefficient (Diamond & Malkov 07). Streaming instability is inefficient for producing large field in the preshock region B Beresnyak & Lazarian 08

35. B j CR shock Bell (2004) proposed a solution based on the current instability

36. Precursor forms in front of the shock and it gets turbulent as precursor interacts with gas density fluctuation

37. MHD scale hydrodynamic cascade Turbulence efficiently generates magnetic fields as shown by Cho et al. 2010

38. The model allows to calculate the parameters of magnetic field Beresnyak, Jones & Lazarian 2010

39. B j CR current instability Take home message 9: Magnetic field generated by precursor -- density fluctuations interaction might be larger than the arising from Bell’s instability