MHD Turbulence and Energetic Particles

1. MHD Turbulence and Energetic Particles Alex Lazarian (Astronomy, Physics and CMSO) Thanks to: H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov , G. Brunetti, V. Petrosian, E. Vishniac, G. Eyink, T. Jones, Pohl etc.

2. Example: Big Power Law revealsKolmogorov spectrum of electron density fluctuations Density fluctuations ISM Turbulence Spectrum Slope ~ -5/3 Electron density spectrum WHAM emission: density fluctuations Scincillations and scattering from Armstrong, Rickett & Spanger 1994 E(k)~k-5/3 pc AU Kolmorogov law for turbulence Chepurnov & Lazarian 2010

3. Turbulent 2nd order Fermi Acceleration Turbulence and shock acceleration Turbulent reconnection induces acceleration This talk shows that turbulence is essential for understanding CR acceleration, makes 4 points: “

4. Point I. Turbulence induces both scattering and the second order Fermi process Magnetic “clouds”

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

6. Turbulence properties determine the diffusion and acceleration • Diffusion in the fluctuating EM fields • Collisionless Fokker-Planck equation • Boltzmann-Vlasov eq • dB, dv<<B0,V(at the scale of resonance) • Fokker-Planck coefficients: Dmm ≈ Dm2/Dt, Dpp ≈ Dp2/Dtare the • fundermental parameters we need. Those are determined by • properties of turbulence! For TTD and gyroresonance, tsc/ tac≈ Dpp / p2Dmm ≈ (VA/v)2

7. B For acceleration and scattering it is important that MHD turbulence is anisotropic Equal velocity correlation contour (Cho & Lazarian 02, 03) Alfven and slow modes (GS95) l|| ~L1/3l^2/3 slow ~k-5/3 ~k-5/3 Alfven anisotropic eddies fast ~k-3/2 fast modes

8. 2. “steep spectrum” E(k ⊥ )~ k ⊥-5/3, k ⊥ ~ L1/3k||3/2 E(k||) ~ k||-2 steeper than Kolmogorov! Less energy on resonant scale Alfven modes (Kolmogorov) Big difference!!! B Beresnyak & Lazarian 08 Alfvenic turbulence marginally scatter/accelerate cosmic rays Streaming instability is suppressed by ambient turbulence: damping versus k 1. “random walk” 2rL B Scattering frequency lperp<< l|| ~ rL l|| (Chandran 2000) B l⊥ eddies Kinetic energy scattering efficiency is reduced Chandran 00, Yan & Lazarian 02, 04

9. Scattering depends on damping Fast modes are identified as major agent of of Cosmic Rays scattering and 2nd order Fermi acceleration fast modes Damping depends on plasma magnetization. Observed secondary elements supports scattering by fast modes (Yan & Lazarian 02, 04). Application to galaxy clusters is in Brunetti & Lazarian (07, 11).

10. Palmer consensus from Bieber et al 1994 Fast modes explain observed flat dependence of mean free path of energy (Palmer consensus) CR Transport in ISM Mean free path (pc) Text WIM halo Kinetic energy Flat dependence of mean free path can occur due to collisionless damping (Yan & Lazarian 2004, 2009).

11. Perpendicular diffusion is determined by magnetic wandering • || > L, CR diffusion is controlled by field line wandering • MA< 1, CRs free stream over distance L, thus D⊥ =R2 /∆t= Lv|| MA4 • MA >1, D⊥ = LA v|| • At smaller scale superdiffusion y~ x3/2 Whether and to what degree CRs diffusion is suppressed depends on || and MA. Lazarian 2006, Yan & Lazarian 2010, Lazarian & Yan 2012

12. To understand the perpendicular diffusion and 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 & Vishniac1999 dB direction changes during cascade Field line wandering Randomization of local B: field line wandering by shearing via Alfven modes: dB/B≈ (V/L)1/2 tk1/2 Randomization of wave vector k: dk/k ≈ (kL)-1/4 V/Vph k Lazarian, Vishniac & Cho 2004 Q B Yan & Lazarian 2004

13. Point II. Turbulence alters processes of Cosmic Ray acceleration in shocks Acceleration in shocks requires scattering of particles back from the upstream region. DownstreamUpstream Magnetic turbulence generated by shock Magnetic fluctuations generated by streaming

14. Transient turbulent magnetic structures explain X-ray observations of young SNRs Chandra Alfvenic turbulence decays in one eddy turnover time (Cho & Lazarian 02), which results in magnetic structures behind the shock being traisient andgenerating filaments of a thickness of 1016-1017cm (Pohl, Yan & Lazarian 05).

15. Precursor forms in front of the shock and it gets turbulent as precursor interacts with gas density fluctuation Beresnyak, Jones & Lazarian 2009

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

17. Magnetic field generated by precursor -- density fluctuations interaction may be larger than the arising from Bell’s instability current instability jCR B

18. Point III. Fast reconnection of 3D weakly turbulent magnetic fields can efficiently accelerate Cosmic Rays LV99 reconnection: 1. Outflow is determined by field wandering. 2. Reconnection is fast with Ohmic resistivity only. B dissipates on a small scale || determined by turbulence statistics. Lazarian & Vishniac (1999) henceforth referred to as LV99

19. Simulations with *different* types of driving confirm LV99 predictions Reconnection rate Lazarian & Vishniac (1999) prediction is Vrec~ Pinj1/2 New simulations Turbulent power Kowal et al. 2012

20. In LV99 reconnection model energetic particles get accelerated by First Order Fermi mechanism (Similar to Drake 2006). Cosmic rays get spectrum steeper than from shocks From Lazarian 05 Published in De Gouveia Dal Pino & Lazarian 2003 Effects of compressibility see Drury 2012

21. Convergence between the plasma-based reconnection and LV99 model is evident! Paradigm 1999 LV99 model Hall effect is required Hall effect is not required Paradigm 2012 (Fully 3D, turbulence) 3D simulations without turbulence show transfer to turbulent state (e.g. Karimabadi 2012) Drake et al. 2006 Tearing reconnection (Hall effect is not required )

22. MHD calculations reproduce parallel acceleration in 2D PIC calculations by Drake et al and go beyond Zoom in into itrajectories Regular energy increase Multiple reconnection layers are used to produce volume reconnection. Kowal et al. 2010

23. First order Fermi acceleration happens also for perpendicular components Converging flow

24. Perpendicular First order Fermi acceleration may dominate in 3D reconnection in the presence of turbulence Kowal et al. 2012

25. Acceleration in sites of turbulent reconnection may be important for many astrophysical settings. *Selected* ones: Acceleration of anomalous cosmic rays (Lazarian & Opher 2009, Drake et al. 2010) Acceleration of cosmic rays in heliotail (Lazarian & Desiati 2010) Acceleration of particles during gamma ray bursts (Lazarian et al. 2003, Zhang & Yan 2011)

26. Turbulence and its effects are essential for understanding cosmic ray spectrum Recent example: turbulent reconnection allows a new First order Fermi acceleration mechanism

27. Non-linear extension of QLT are necessary to describe diffusion and acceleration, especially by TTD mechanism Numerical testing Momentum diffusion from adiabatic invariant TTD scattering by slow modes broadened resonance function Basis of Nonlinear QLT (Yan & Lazarian 2008) Applied for Solar acceleration in Yan, Lazarian & Petrosian 2008 Beresnayk, Yan & Lazarian 2011

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

29. What does happen: parallel or perpendicular First order Fermi acceleration? Lazarian 2005 Parallel acceleration (similar to that In Drake et al. 2006) Perpendicular acceleration

30. VCA and VCS are our new techniques to study supresonic turbulence. Sparsely sampled data can be delt with VCS. VCS Developed in Lazarian & Pogosyan 00, 06, 08

31. VCA and VCS techniques (Lazarian & Pogosyan 00, 04, 06, 08) reveal turbulence velocity spectra in agreement with expectations for supersonic turbulence Expectations for supersonic turbulence Density spectrum gets shallow Velocity spectrum gets steep Kowal, Lazarian & Beresnyak 2007 Kowal & Lazarian 2010 VCS gets for high latitude galactic HI Ev~k-1.87 (Chepurnov et al.08,10) for 13CO for the NGC 1333 Ev~k1.85 (Padoan et al. 09) indicating supersonic turbulence. Density is shallow ~k-0.8 Selected results for the techniques

32. Big Implication: LV99 means that magnetic field in turbulent fluids is not frozen in Hannes Alfven Violation of magnetic field frozen in condition in turbulent fluids discussed in Eyink (2010, 2011). The equivalence of this to LV99 approach was demonstrated in Eyink, Lazarian & Vishniac 2011. Recent numerical evidence is in Eyink et al. (2012, Nature, submitted).

33. Bell (2004) proposed a solution based on the current instability jCR B shock

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

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