MHD turbulence: Consequencies and Techniques to study Huirong Yan Supervisor: Alex Lazarian University of Wisconsin-Madison Predoctoral work in Stanford (04-05)

Directions of Research Cosmic Ray (CR) transport and acceleration (Yan & Lazarian 2002 Physical Review Letters, Yan & Lazarian 2004 ApJ Lazarian, Cho & Yan 2003 review, Recent Res. Dev. Astrophys. Cho, Lazarian & Yan 2002 review, ASP) Interstellar dust dynamics and their implications (Yan, Lazarian & Draine 2004 ApJ,Yan & Lazarian 2003 ApJ, Lazarian & Yan 2002 ApJ, Lazarian & Yan 2004 review, ASP, Yan & Lazarian 2004 Texas Symposium)

Polarimetric study of interstellar and circumstellar magnetic fields by atomic alignment (Yan & Lazarian submitted to ApJ, Yan & Lazarian 2004 Polarimetry Symposium, Lazarian & Yan 2005 review) Solar physics and others Yan, Petrosian & Lazarian 2005 submitted, Suzuki, Yan, Lazarian & Cassenelli 2005 submitted, Pohl, Yan & Lazarian 2005 ApJL, Lazarian, Petrosian, Yan & Cho 2003 review) Directions of Research (cont.)

Cosmic ray Scattering Propagation Isotropy Light elements: Li, Be, B, etc Long age Post-shockPre-shockregion 1st order Fermi 2nd order Fermi Acceleration Shock front Magnetic “clouds”

Where does  B come from? MHD turbulence! Re ~VL/ ~10 10 >> 1 ~ r L v th, v th < V, r L << L Cosmic Raysinterstellar medium EM perturbations,  E,  (local CR frame) Interstellar medium is magnetized and turbulent! Cosmic ray physics is a general problem (ISM,  ray burst, solar flares). Here we are concentrated on ISM. Cosmic ray transport

Diffusion in the fluctuating EM fields CollisionlessFokker-Planck equation Boltzmann-Vlasov eq   B<<B 0 (at the scale of scattering) Fokker-Planck coefficients: D , D  p, D pp are the fundermental parameters we need! They are primarily determined by the statistical properties of MHD turbulence! How do we study the scattering?

Examples of MHD modes (P mag > P gas ) Alfven mode (v=V A cos  ) incompressible; restoring force=mag. tension k B slow mode (v=c s cos  ) fast mode (v=V A ) restoring force = P mag + P gas B k B restoring force = |P mag -P gas |

Models of MHD turbulence Earlier models Slab model: Only MHD modes propagating along the magnetic field are counted. Kolmogorov turbulence: isotropic, with 1D spectrum E(k)~k -5/3 Realistic MHD turbulence ( Cho & Lazarian 2002, 2003 ) 1. Alfven and slow modes: Goldreich-Sridhar 95 scaling 2. Fast modes: isotropic, similar to accoustic turbulence

Anisotropy of MHD modes Alfven and slow modes fast modes Equal velocity correlation contour contourB

Resonant scattering 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). So, k ||,res ~  /v = 1/r L Resonance mechanism B

Scattering by Alfvenic turbulence Alfven modes do not contribute to particle scattering if energy is injected from large scale! 2r L 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 in resonant scaleeddies B l || llll 1. “ random walk” B

Alfven modes are inefficient. Fast modes dominate CR scattering in spite of damping (Yan & Lazarian 2002). Scattering by MHD turbulence Scattering frequency (Kolmogorov) Alfven modes Big difference!!! Fast modes Depends on damping

Damping of fast modes Viscous damping Collisionless damping Ion-neutral damping increase with both plasma  and the angle  between k and B. Cutoff wave number k c : defined as the scales on which damping rate is equal to cascading rate  k -1 =   (k c v k ) 2 = (k c L) 1/2 V 2 /V ph.

  complication: randomization of  during cascade Randomization of wave vector k: dk/k ≈ (kL) -1/4 V/V ph Randomization of local B: field line wandering by shearing via Alfven modes: dB/B ≈ (V/L) 1/2 t k 1/2 = (kL) -1/4 (V ph /V) 1/2 Anisotropic Damping of fast modes Anisotropic damping results in redistribution of fast mode energy (slab geometry). k B  Damping depends on the angle 

Damping of fast modes in various media Cutoff scale in different media Log 10 (k c ) Left: cutoff wave number k c in interstellar medium vs.   Yan & Lazarian 2004)  1au 1pc ISM phases With randomization Without randomization

Transit Time Damping (TTD) Transit time damping (TTD) Compressibility required! Landau resonance condition:  k || v || V ph =  k v || cos  k i) no resonant scale; ii)  k  broadened ii)   k  broadened Landau resonance.

(i) gyroresonance with fast modes is dominant; (ii) scattering rate varies with medium and depends on plasma  What are the scattering rates for different ISM phases? (Yan & Lazarian 2004)

(iii) near 90 o transit time damping (TTD) should be taken into account. Use of  function entails error. (iv) in high  and patially ionized media where gyroresonance doesn’t exist due to severe damping, TTD is dominant. What are the scattering rates for different ISM phases? (Cont.) (Yan & Lazarian 2004)

Streaming instability of CR Acceleration in shocks requires scattering of particles back from the upstream region. Post-shock Pre-shock region 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.

Streaming instability of CR (Cont.) 2. Calculations for weak case (  B<B): With background compressible turbulence ( Yan & Lazarian 2004 ):  max ≈ [n p -1 (V A /V) 0.5 (Lc   /V 2 ) 0.5 ] 1/1.1 E 0 This gives  max ≈ 20GeV for HIM. This is similar to the estimate obtained with background Alfvenic turbulence ( Farmer & Goldreich 2004 ) MHD turbulence can suppress streaming instability ( Yan & Lazarian 2002 ).

3. Strong case (e.g. shocks): Magnetic field itself can be amplified through inverse cascade. As a result,  B > B 0, the growth rate becomes higher in this case. And the streaming instability operates till higher energies (Yan & Lazarian 2004):  max ≈ (a  (LeB 0 ) 0.5 U 3 /(m 0.5 V 2 c 2 )) 1/(0.5+a )E 0, where  is the ratio of the pressure of CRs at the shock and the upstream momentum flux entering the shock front, U is the shock front speed, a-4 is the spectrum index of CRs at the shock front. This gives  max ≈ (t/kyr) -9/4 for HIM. Shock acceleration should be revised. Cosmic Ray confinement in galaxies should be revised. Streaming instability of CR (Cont.)

Applications to stellar physics heating by collisionless damping is dominant in rotating stars ( Suzuki, Yan, Lazarian, & Casseneli 2005 ). B Acceleration by fast modes is an important mechanism to generate high energy particles in Solar flares ( Yan, Petrosian & Lazarian 2005 );

Thermal damping of turbulence in solar flares Dampin cutoff scale of fast modes The angle between k and B From Suzuki, Yan, Lazarian, Cassenelli (2005)

Timescalse for cascade adn linear ddamping Wave number Nonthermal damping of turbulence in solar flares

Nonthermal damping (cont.) Dampin cutoff scale of fast modes The angle between k and B Transit time damping with nonthermal particle can dominate damping of fast modes with large pitch angles

Nothermal damping (Cont.) Damping by gyroresonance is subdominant. Timescalse for cascade adn linear ddamping Wave number

Acceleration of dust grains  ew  mechanism:  Gyroresonance (Yan & Lazarian 2003) The dynamics of turbulence ought to be taken into account, resulting in resonance broadening. Grain velocities in various media were calculated in Yan, Lazarian & Draine (2004) 1km/s!

Shattering and coagulation thresholds Acceleration by turbulence is most effcient Grains get supersonic Grains may get aligned Turbulence mixing of grains is efficient Correlation between turbu- lence and grain size

Toy model: Definition: Atomic Alignment is defined here as differential occupation of the fine or hyperfine sublevels of the ground state. Atomic alignment is induced by anisotropic radiation. Species to align: virtually most atoms with fine or hyperfine structures. (optical and UV lines) Atomic alignment (work in progress)

Requirement for alignment : Requirement for alignment : Can unpolarized light induce alignment? Yes, magnetic substates with opposite “M F ” will be symmetrically populated, but alignment will be present. Major requirement: anisotropic radiation (usual for astrophysics) Has atomic alignment been observed? In laboratory Na alignment has been studied in relation to maser research (Brossel et al 1952, Hawkins 1955). Why hyperfine structure (if exists) is important? Hyperfine interaction causes substantial precession of J about F before spontaneous emission occurs (Walkup 1982). Presence of nuclear moment splits the ground level and allows alignment in the ground state.

NaINVAlIIIHINIOII OICrIICIIOIVCIOIII Examples of alignable species (Yan & Lazarian 2005)  L –Larmor frequency R-photon arrival rate A-Einstein coefficient Range of applicablity:

Role of magnetic field Magnetic field causes precession of atoms and therefore changes the alignment of atoms caused by radiation.M=2M=1 M=0 M=-1 M=-2 z BF  radiationatoms Angular momentum

Quantum Electrodynamics calculations Main object: density tensor:  k q  2 : dipole moment  4 : quardripole moment They can be obtained from statistical equilibrium equation of the upper state and ground state of an atom.

Quantum Electrodynamics calculations (Cont.)

Theoretical and observational frame (B) Left: Radiation geometry and the polarization vectors; Right: Transformation from observational frame to theoretical frame by two successive rotations specified by Euler angles (  B,  )

Differential population of ground state The density tensor components  2,4 of ground state of Cr II line 6S 5/2 6P 7/2 ; left: without multiplet effect, only the transition between the two levels are counted; right: with multiplet effect. rrrr rrrr  

The observed polarization depends on both line of sight and the direction of incident light. Polarization vs. the direction of incident light for fixed line of sight  =90 o and  =0 o. Polarization of emission lines  polar angle  azimuthal angle rrrr rrrr p

Application: magnetic fields in the wake of a comet (a) (a) Resonance scattering of solar light by sodium tail from comet; (b) v (b) MHD simulations of comet’s wake; (c) Polarization caused by sodium aligned in the comet wake. (c) y (r comet ) E1

Sensitive to smaller scale fluctuations. 3D information of magnetic field can be obtained from atomic alignment. Provide independent test to grain alignment theory. In comparison with dust alignment:

Summary of the most important results for PhD work Fast MHD modes are identified as the major scattering agent for Galactic cosmic rays. Scattering of cosmic rays depends on the medium. Streaming instability is partially suppressed by turbulence. Results are applied to solar physics. Gyroresonance is identified as a new acceleration mechanism, which can drive grains to supersonic velocities. This can have implications in various topics, including grain alignment, grain mixing and CR abundance, etc. Atomic alignment is identified as a new tool to study 3D geometry of interstellar and circumstellar magnetic fields.  agnetic field study Cosmic ray transport Dust dynamics